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635 results on '"Rassias, Michael Th."'

1. The behaviour of a certain additive function in large intervals between consecutive primes

Author

Rassias, Michael Th.

Subjects
Mathematics - Number Theory
Abstract

We investigate the behaviour of a certain additive function depending on prime divisors of specific integers lying in large gaps between consecutive primes. The result is obtained by a combination of results and ideas related to large gaps between primes and the Erd\"os-Kac theorem, especially the Kubilius model from Probabilistic Number Theory.

Published
2024

2. Recent results on large gaps between primes

Author

Rassias, Michael Th.

Subjects
Mathematics - Number Theory
Abstract

One of the themes of this paper is recent results on large gaps between primes. The first of these results has been achieved in the paper [12] by Ford, Green, Konyagin and Tao. It was later improved in the joint paper [13] of these four authors with Maynard. One of the main ingredients of these results are old methods due to Erd\H{o}s and Rankin. Other ingredients are important breakthrough results due to Goldston, Pintz and Yildirim [15, 16, 17], and their extension by Maynard on small gaps between primes. All these previous results are discussed shortly. The results on the appearance of $k$-th powers of primes contained in those large gaps, obtained by the author in joint work with Maier [23, 24, 25] are based on a combination of the results just described with the matrix method of Maier., Comment: arXiv admin note: substantial text overlap with arXiv:1412.5029, arXiv:1511.04468 by other authors

Published
2024

4. Prime Avoidance Property of $k$-th Powers of Piatetski-Shapiro Primes

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Number Theory, 11P32, 11N05, 11A63
Abstract

In previous papers the authors established the prime avoidance property of $k$-th powers of prime numbers and of prime numbers within Beatty sequences. In this paper the authors consider $k$-th powers of Piatetski-Shapiro primes.

Published
2023

5. On a Reverse Hilbert-Type Inequality in the Whole Plane with Multi-Parameters

Author

Rassias, Michael Th., Yang, Bicheng, Raigorodskii, Andrei, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Advisory Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, Rassias, Michael Th., editor, and Zographopoulos, Nikolaos B., editor

Published
2023
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6. A Unified Approach to Extended General Quasi Variational Inclusions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Advisory Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, Rassias, Michael Th., editor, and Zographopoulos, Nikolaos B., editor

Published
2023
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7. The ternary Goldbach problem with a prime with a missing digit and primes of special types

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Number Theory
Abstract

Let $$\gamma^*:=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx 0.919\ldots)\:,\ \gamma^*<\frac{1}{c_0}\leq 1\:.$$ Let $\gamma^*<\gamma_0\leq 1$, $c_0=1/\gamma_0$ be fixed. Let also $a_0\in\{0,1,\ldots, 9\}$. In [23] we proved on assumption of the Generalized Riemann Hypothesis (GRH), that each sufficiently large odd integer $N_0$ can be represented in the form $$N_0=p_1+p_2+p_3\:,$$ where for $i=2, 3$ the primes $p_i$ are Piatetski-Shapiro primes - primes of the form $p_i=[n_i^{c_0}]$, $n_i\in\mathbb{N}$ - whereas the decimal expansion of $p_1$ does not contain the digit $a_0$. In this paper we replace one of the Piatetski-Shapiro primes $p_2$ and $p_3$ by primes of the type $$p=x^2+y^2+1\:.$$, Comment: arXiv admin note: text overlap with arXiv:2006.07873

Published
2021

9. The ternary Goldbach problem with two Piatetski-Shapiro primes and a prime with a missing digit

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Number Theory, 11P32, 11N05, 11A63
Abstract

Let $$\gamma^*=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx 0.919\ldots)\:.$$ Let $\gamma^*<\gamma_0\leq 1$, $c_0=1/\gamma_0$ be fixed. Let also $a_0\in\{0,1,\ldots, 9\}$.\\ We prove on assumption of the Generalized Riemann Hypothesis that each sufficiently large odd integer $N_0$ can be represented in the form $$N_0=p_1+p_2+p_3\:,$$ where the $p_i$ are of the form $p_i=[n_i^{c_0}]$, $n_i\in\mathbb{N}$, for $i=1,2$ and the decimal expansion of $p_3$ does not contain the digit $a_0$.\\ The proof merges methods of J. Maynard from his paper on the infinitude of primes with restricted digits, results of A. Balog and J. Friedlander on Piatetski-Shapiro primes and the Hardy-Littlewood circle method in two variables. This is the first result on the ternary Goldbach problem with primes of mixed type which involves primes with missing digits.

Published
2020

11. A Viscosity Iterative Method with Alternated Inertial Terms for Solving the Split Feasibility Problem

Author

Liu, Lulu, Dong, Qiao-Li, Wang, Shen, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Advisory Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Nikeghbali, Ashkan, editor, Raigorodskii, Andrei M., editor, and Rassias, Michael Th., editor

Published
2022
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15. On some links between the generalised Lucas pseudoprimes of level k

Author

Andrica Dorin, Bagdasar Ovidiu, and Rassias Michael Th.

Subjects
generalised lucas sequences, jacobi symbol, pseudoprimality, pseudoprimality of level k, primary 11a51, secondary 11b39, 11b50, Mathematics, QA1-939
Abstract

Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences. In this paper we first establish new arithmetic properties of the generalized Lucas and Pell-Lucas sequences. Then we study the recent notion of generalized Pell and Pell-Lucas pseudo-primes of level k, and find inclusions between the sets of pseudoprimes on different levels. In this process we extend several results concerning Fibonacci, Lucas, Pell, and Pell-Lucas sequences.

Published
2023
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19. Weak Pseudoprimality Associated with the Generalized Lucas Sequences

Author

Andrica, Dorin, Bagdasar, Ovidiu, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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20. General Preinvex Functions and Variational-Like Inequalities

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Mohsen, Bandar, Rassias, Michael Th., Raigorodskii, Andrei, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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21. Interpolation of the Zech’s Logarithm: Explicit Forms

Author

Meletiou, Gerasimos C., Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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22. Exponential Type Operators

Author

Gupta, Vijay, Rassias, Michael Th., Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Jorgensen, Palle, Series Editor, Li, Tatsien, Series Editor, Melnik, Roderick, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Reichel, Lothar, Series Editor, Tschinkel, Yuri, Series Editor, Yin, George, Series Editor, Zhang, Ping, Series Editor, Gupta, Vijay, and Rassias, Michael Th.

Published
2021
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23. Difference Between Operators

Author

Gupta, Vijay, Rassias, Michael Th., Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Jorgensen, Palle, Series Editor, Li, Tatsien, Series Editor, Melnik, Roderick, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Reichel, Lothar, Series Editor, Tschinkel, Yuri, Series Editor, Yin, George, Series Editor, Zhang, Ping, Series Editor, Gupta, Vijay, and Rassias, Michael Th.

Published
2021
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24. Modifications of Certain Operators

Author

Gupta, Vijay, Rassias, Michael Th., Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Jorgensen, Palle, Series Editor, Li, Tatsien, Series Editor, Melnik, Roderick, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Reichel, Lothar, Series Editor, Tschinkel, Yuri, Series Editor, Yin, George, Series Editor, Zhang, Ping, Series Editor, Gupta, Vijay, and Rassias, Michael Th.

Published
2021
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25. Cotangent sums related to the Riemann Hypothesis for various shifts of the argument

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

One of the approaches to the Riemann Hypothesis is the Nyman-Beurling criterion. Cotangent sums play a significant role. Here we investigate the values of these cotangent sums for various shifts of the argument.

Published
2018

26. Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis. These sums contain the M\"obius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comparison to other sums containing the M\"obius function. The bound is smaller than the trivial bound - essentially the number of terms - by a fixed power of that number. The exponent is made explicit. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series., Comment: arXiv admin note: substantial text overlap with arXiv:1705.09921

Published
2018

27. The error for the second moment of cotangent sums related to the Riemann Hypothesis

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In various papers the authors have derived asymptotics for moments of certain cotangent sums related to the Riemann Hypothesis. S. Bettin has given an upper bound for the error term in these asymptotic results. In the present paper the authors establish a lower bound for the error term for the second moment.

Published
2018

28. Prime Avoidance Property of k-th Powers of Prime Numbers with Beatty Sequence

Author

Maier, Helmut, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Giannessi, Franco, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Raigorodskii, Andrei M., editor, and Rassias, Michael Th., editor

Published
2020
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31. Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs, 30C15, 11M26, 42A16, 42A20
Abstract

We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the M\"obius function. The estimate is remarkably sharp in comparison to estimates of other sums containing the M\"obius function. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.

Published
2017

32. A criterion related to the Riemann Hypothesis

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs, 30C15, 11M26
Abstract

A crucial role in the Nyman-Beurling-B\'aez-Duarte approach to the Riemann Hypothesis is played by the distance \[ d_N^2:=\inf_{A_N}\frac{1}{2\pi}\int_{-\infty}^\infty\left|1-\zeta A_N\left(\frac{1}{2}+it\right)\right|^2\frac{dt}{\frac{1}{4}+t^2}\:, \] where the infimum is over all Dirichlet polynomials $$A_N(s)=\sum_{n=1}^{N}\frac{a_n}{n^s}$$ of length $N$. In this paper we investigate $d_N^2$ under the assumption that the Riemann zeta function has four non-trivial zeros off the critical line. Thus we obtain a criterion for the non validity of the Riemann Hypothesis.

Published
2017

33. From a cotangent sum to a generalized totient function

Author

Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs, 33B10, 11L03, 11N37
Abstract

In this paper we investigate a certain category of cotangent sums and more specifically the sum $$\sum_{m=1}^{b-1}\cot\left(\frac{\pi m}{b}\right)\sin^{3}\left(2\pi m\frac{a}{b}\right)\:$$ and associate the distribution of its values to a generalized totient function $\phi(n,A,B)$, where $$\phi(n,A,B):=\sum_{\substack{A\leq k \leq B \\ (n,k)=1}}1\:.$$ One of the methods used consists in the exploitation of relations between trigonometric sums and the fractional part of a real number.

Published
2017

34. EQUIVALENT CONDITIONS OF A REVERSE HILBERT - TYPE INTEGRAL INEQUALITY IN THE WHOLE PLANE AND APPLICATIONS.

Author

Rassias, Michael Th. and Bicheng Yang

Abstract

In the present paper we establish a few equivalent conditions of a reverse Hilbert-type integral inequality with a general non-homogeneous kernel in the whole plane. In the form of applications, we deduce a few equivalent conditions of a reverse Hilbert-type integral inequality with a general homogeneous kernel in the whole plane. We also consider some particular cases and examples. [ABSTRACT FROM AUTHOR]

Published
2024
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35. On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms

Author

Yang, Bicheng, Andrica, Dorin, Bagdasar, Ovidiu, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Parasidis, Ioannis N., editor, Providas, Efthimios, editor, and Rassias, Themistocles M., editor

Published
2021
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36. Characterizations of Higher Order Strongly Generalized Convex Functions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, and Rassias, Themistocles M., editor

Published
2021
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38. Introduction

Author

Yang, Bicheng, Rassias, Michael Th., Jorgensen, Palle, Series Editor, Melnik, Roderick, Series Editor, Reichel, Lothar, Series Editor, Yin, George, Series Editor, Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Li, Tatsien, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Tschinkel, Yuri, Series Editor, Zhang, Ping, Series Editor, Yang, Bicheng, and Rassias, Michael Th.

Published
2019
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39. Equivalent Statements of Two Kinds of Hardy-Type Integral Inequalities

Author

Yang, Bicheng, Rassias, Michael Th., Jorgensen, Palle, Series Editor, Melnik, Roderick, Series Editor, Reichel, Lothar, Series Editor, Yin, George, Series Editor, Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Li, Tatsien, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Tschinkel, Yuri, Series Editor, Zhang, Ping, Series Editor, Yang, Bicheng, and Rassias, Michael Th.

Published
2019
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40. Equivalent Property of the Reverse Hardy-Type Integral Inequalities

Author

Yang, Bicheng, Rassias, Michael Th., Jorgensen, Palle, Series Editor, Melnik, Roderick, Series Editor, Reichel, Lothar, Series Editor, Yin, George, Series Editor, Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Li, Tatsien, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Tschinkel, Yuri, Series Editor, Zhang, Ping, Series Editor, Yang, Bicheng, and Rassias, Michael Th.

Published
2019
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41. Equivalent Statements of Hilbert-Type Integral Inequalities

Author

Yang, Bicheng, Rassias, Michael Th., Jorgensen, Palle, Series Editor, Melnik, Roderick, Series Editor, Reichel, Lothar, Series Editor, Yin, George, Series Editor, Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Li, Tatsien, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Tschinkel, Yuri, Series Editor, Zhang, Ping, Series Editor, Yang, Bicheng, and Rassias, Michael Th.

Published
2019
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42. Equivalent Statements of the Reverse Hilbert-Type Integral Inequalities

Author

Yang, Bicheng, Rassias, Michael Th., Jorgensen, Palle, Series Editor, Melnik, Roderick, Series Editor, Reichel, Lothar, Series Editor, Yin, George, Series Editor, Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Li, Tatsien, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Tschinkel, Yuri, Series Editor, Zhang, Ping, Series Editor, Yang, Bicheng, and Rassias, Michael Th.

Published
2019
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43. Integral Type Operators and Moments

Author

Gupta, Vijay, Rassias, Michael Th., Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Jorgensen, Palle, Series Editor, Li, Tatsien, Series Editor, Melnik, Roderick, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Reichel, Lothar, Series Editor, Tschinkel, Yuri, Series Editor, Yin, George, Series Editor, Zhang, Ping, Series Editor, Nonato, Luis Gustavo, Editorial Board Member, Silva, Paulo J. S., Editorial Board Member, Gupta, Vijay, and Rassias, Michael Th.

Published
2019
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44. Approximation Properties of Certain Operators

Author

Gupta, Vijay, Rassias, Michael Th., Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Jorgensen, Palle, Series Editor, Li, Tatsien, Series Editor, Melnik, Roderick, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Reichel, Lothar, Series Editor, Tschinkel, Yuri, Series Editor, Yin, George, Series Editor, Zhang, Ping, Series Editor, Nonato, Luis Gustavo, Editorial Board Member, Silva, Paulo J. S., Editorial Board Member, Gupta, Vijay, and Rassias, Michael Th.

Published
2019
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45. Some Positive Linear Operators and Moments

Author

Gupta, Vijay, Rassias, Michael Th., Bellomo, Nicola, Series Editor, Benzi, Michele, Series Editor, Jorgensen, Palle, Series Editor, Li, Tatsien, Series Editor, Melnik, Roderick, Series Editor, Scherzer, Otmar, Series Editor, Steinberg, Benjamin, Series Editor, Reichel, Lothar, Series Editor, Tschinkel, Yuri, Series Editor, Yin, George, Series Editor, Zhang, Ping, Series Editor, Nonato, Luis Gustavo, Editorial Board Member, Silva, Paulo J. S., Editorial Board Member, Gupta, Vijay, and Rassias, Michael Th.

Published
2019
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47. Asymptotics for moments of certain cotangent sums for arbitrary exponents

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In this paper we extend a result on the asymptotics of moments of certain cotangent sums associated to the Estermann and Riemann zeta functions established in a previous paper for integer exponents to arbitrary positive real exponents.

Published
2016

48. The ternary Goldbach problem with a prime and two isolated primes

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Number Theory
Abstract

In the present paper we prove that under the assumption of the GRH (Generalized Riemann Hypothesis) each sufficiently large odd integer can be expressed as the sum of a prime and two isolated primes.

Published
2016

49. Asymptotics for moments of certain cotangent sums

Author

Maier, Helmut and Rassias, Michael Th.

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In this paper we improve a result on the order of magnitude of certain cotangent sums associated to the Estermann and the Riemann zeta functions.

Published
2016

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