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Your search keyword '"Dirichlet character"' showing total 15 results
Start Over Descriptor "Dirichlet character" Journal mathematical notes
15 results on '"Dirichlet character"'

1. Decomposition of spaces of modular forms.

Author

Voskresenskaya, G.

Subjects
*MATHEMATICAL forms, *MATHEMATICS theorems, *CONGRUENCE lattices, *DIRICHLET forms, *EISENSTEIN series
Abstract

Structural theorems for spaces of modular forms with respect to congruence subgroups are proved. The Dedekind η-function plays an important role in our study. [ABSTRACT FROM AUTHOR]

Published
2016
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2. An Elliott-type theorem for twists of L-functions of elliptic curves.

Author

Laurinčikas, A.

Subjects
*ELLIPTIC curves, *MATHEMATICS theorems, *DIRICHLET series, *PRIME numbers, *DISTRIBUTION (Probability theory)
Abstract

A limit theorem involving an increasing modulus of the character is obtained for twists with the Dirichlet character of L-functions of elliptic curves. [ABSTRACT FROM AUTHOR]

Published
2016
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3. On monochromatic solutions of some nonlinear equations in ℤ/ pℤ.

Author

Shkredov, I. D.

Subjects
*NONLINEAR evolution equations, *RINGS of integers, *RAMSEY theory, *DIRICHLET forms, *FOURIER transforms, *TRIGONOMETRIC sums
Abstract

Let the set of positive integers be colored in an arbitrary way in finitely many colors (a 'finite coloring'). Is it true that, in this case, there are x, y ∈ ℤ such that x + y, xy, and x have the same color? This well-known problem of the Ramsey theory is still unsolved. In the present paper, we answer this question in the affirmative in the group ℤ/ pℤ, where p is a prime, and obtain an even stronger density result. [ABSTRACT FROM AUTHOR]

Published
2010
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4. A note on Burgess's estimate.

Author

Gallagher, P. X. and Montgomery, H. L.

Subjects
*ESTIMATION theory, *MAXIMAL functions, *DIRICHLET forms, *DIRICHLET integrals, *LEGENDRE'S functions, *RIEMANN hypothesis
Abstract

By introducing the Rademacher-Menchov device, we prove 'maximal' analogs of principal bounds of character sums. This allows us to present the Burgess method so as to separate the main idea of this method from the technical issues. [ABSTRACT FROM AUTHOR]

Published
2010
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5. On the joint universality of Lerch zeta functions.

Author

Laurinčikas, A.

Subjects
*ZETA functions, *ANALYTIC functions, *PROBABILITY measures, *INTEGRAL functions, *MEASURE theory
Abstract

In the paper, a Voronin-type joint universality theorem for Lerch zeta functions is obtained under weaker assumptions than those in A. Laurinčikas and K. Matsumoto, 'Joint value distribution theorems on Lerch zeta-functions. III,' in Analytic and Probabilistic Methods in Number Theory (TEV, Vilnius, 2007), pp. 87-98. [ABSTRACT FROM AUTHOR]

Published
2010
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6. Enlarged major arcs in additive problems.

Author

Jianya Liu

Subjects
*GOLDBACH conjecture, *NUMERICAL functions, *DIRICHLET integrals, *NUMERICAL solutions to the Dirichlet problem, *EXPONENTIAL sums, *PRIME numbers
Abstract

Enlarged major arcs in the Waring-Goldbach problem are studied by using large sieve estimates for Dirichlet polynomials and estimates for exponential sums over primes. [ABSTRACT FROM AUTHOR]

Published
2010
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7. On a problem of Karatsuba.

Author

Gritsenko, S. A.

Subjects
*COMBINATORICS, *INTERVAL analysis, *COMPLEX variables, *CARDINAL numbers
Abstract

We obtain lower bounds for the fractional moments of linear combinations of analogs of the Hardy function. In addition, we apply these estimates to the Karatsuba problem of finding a lower bound for the number of zeros of the linear combination of analogs of Hardy functions on the interval (0, T]. [ABSTRACT FROM AUTHOR]

Published
2010
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8. Functional independence of periodic Hurwitz zeta functions.

Author

Laurinchikas, A.

Subjects
*ZETA functions, *ARTIN'S conjecture, *EULER products, *SELBERG trace formula, *RATIONAL numbers, *REAL numbers, *NATURAL numbers
Abstract

We prove functional independence and joint functional independence for a set of Hurwitz zeta functions with periodic coefficients and parameters algebraically independent over the field of rational numbers. [ABSTRACT FROM AUTHOR]

Published
2008
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9. The Concentration Function of Additive Functions with Special Weight.

Author

Timofeev, N.M. and Khripunova, M.B.

Subjects
*CONCENTRATION functions, *ADDITIVE functions, *DIVISOR theory, *DIRICHLET series, *MATHEMATICAL inequalities, *INTEGRALS
Abstract

Suppose that g(n) is an additive real-valued function, W(N) = 4+min λ(λ² + ∑p

Published
2004

10. The Concentration Function of Additive Functions with Nonmultiplicative Weight.

Author

Timofeev, N. M. and Khripunova, M. B.

Subjects
*CONCENTRATION functions, *MATHEMATICAL functions, *NUMERICAL analysis, *MATHEMATICS
Abstract

Suppose that g(n) is a real-valued additive function and \tau(n) is the number of divisors of n. In this paper, we prove that there exists a constant C such that \sup_a\sum\Sb n where W(N) =4+\min_\lambda\biggl(\lambda^2+\sum_{p In particular, it follows from this result that \sup_a\bigl|\bigl\ m,n:mn The implicit constant is absolute. [ABSTRACT FROM AUTHOR]

Published
2004
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11. A note on Burgess’s estimate

Author

P. X. Gallagher and Hugh L. Montgomery

Subjects
Algebra, symbols.namesake, Character (mathematics), General Mathematics, Principal (computer security), symbols, Legendre symbol, Dirichlet character, Mathematics
Abstract

By introducing the Rademacher-Menchov device, we prove “maximal” analogs of principal bounds of character sums. This allows us to present the Burgess method so as to separate the main idea of this method from the technical issues.

Published
2010

12. On a problem of Karatsuba

Author

S. A. Gritsenko

Subjects
Euler function, General Mathematics, Dirichlet L-function, Karatsuba algorithm, Function (mathematics), Upper and lower bounds, Dirichlet character, Algebra, Combinatorics, Z function, symbols.namesake, symbols, Linear combination, Mathematics
Abstract

We obtain lower bounds for the fractional moments of linear combinations of analogs of the Hardy function. In addition, we apply these estimates to the Karatsuba problem of finding a lower bound for the number of zeros of the linear combination of analogs of Hardy functions on the interval (0, T].

Published
2010

14. The Concentration Function of Additive Functions with Special Weight

Author

M. B. Khripunova and N. M. Timofeev

Subjects
Discrete mathematics, Coprime integers, General Mathematics, Prime factor, Concentration function, Dirichlet character, Mathematics
Abstract

Suppose that $${g\left( n \right)}$$ is an additive real-valued function, W(N) = 4+ $$\mathop {\min }\limits_\lambda $$ ( λ2 + $$\sum\limits_{p < N} {\frac{1}{2}} $$ min (1, ( g(p) - λlog p)2), E(N) = 4+1 $$\sum\limits_{\mathop {p < N,}\limits_{g(p) \ne 0} } {\frac{1}{p}.} $$ In this paper, we prove the existence of constants C1, C2 such that the following inequalities hold: \(\mathop {\sup }\limits_a \geqslant \left| {\left\{ {n, m, k: m, k \in \mathbb{Z},n \in \mathbb{N},n + m^2 + k^2 } \right.} \right. = \left. {\left. {N,{\text{ }}g(n) \in [a,a + 1)} \right\}} \right| \leqslant \frac{{C_1 N}}{{\sqrt {W\left( N \right)} }},\)\(\mathop {\sup }\limits_a \geqslant \left| {\left\{ {n, m, k: m, k \in \mathbb{Z},n \in \mathbb{N},n + m^2 + k^2 } \right.} \right. = \left. {\left. {N,{\text{ }}g(n) = a} \right\}} \right| \leqslant \frac{{C_2 N}}{{\sqrt {E\left( N \right)} }},\). The obtained estimates are order-sharp.

Published
2004

15. The Concentration Function of Additive Functions with Nonmultiplicative Weight

Author

M. B. Khripunova and N. M. Timofeev

Subjects
Discrete mathematics, Coprime integers, General Mathematics, Additive function, Prime factor, Divisor function, Concentration function, Dirichlet character, Mathematics
Abstract

Suppose that g(n) is a real-valued additive function and τ(n) is the number of divisors of n. In this paper, we prove that there exists a constant C such that \(\sup \limits_a \sum\limits_{n

Published
2004

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