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3 results on '"Pablo Andres Panzone"'

1. Integrales de ciertas series de Dirichlet

Author

Pablo Andres Panzone

Subjects
symbols.namesake, Pure mathematics, Dirichlet Series, General Mathematics, symbols, Integrales, Integrals, Dirichlet series, Series de Dirichlet, Mathematics
Abstract

We compute in closed form the integrals of certain expressions involving a class of Dirichlet series. This is a generalization of a formula of Jonathan Borwein to a problem stated (and solved) by A. Ivić. Resumen: Calculamos en forma cerrada integrales de ciertas expresiones que involucran una clase de series de Dirichlet. Esto es una generalización de una fórmula de Jonathan Borwein a un problema enunciado (y resuelto) por A. Ivić.

Published
2020

2. Formulas for the Riemann zeta-function and certain Dirichlet series

Author

Pablo Andres Panzone

Subjects
Pure mathematics, Mathematics::Complex Variables, Mathematics::General Mathematics, Matemáticas, Mathematics::Number Theory, Applied Mathematics, Mathematics::Classical Analysis and ODEs, Mathematics::Spectral Theory, Riemann zeta function, Ramanujan's sum, Matemática Pura, symbols.namesake, Riemann hypothesis, Fourier transform, symbols, DIRICHLET SERIES, RIEMANN ZETA-FUNCTION, FOURIER TRANSFORM, Analysis, Dirichlet series, CIENCIAS NATURALES Y EXACTAS, Mathematics
Abstract

Using formulas of G. Hardy and S. Ramanujan we give several integral formulas for the Riemann zeta function and two Dirichlet series. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina

Published
2018

3. On a Formula of S. Ramanujan

Author

Pablo Andres Panzone

Subjects
Pure mathematics, Matemáticas, General Mathematics, Ramanujan summation, Ramanujan, Rational function, Ramanujan's congruences, Ramanujan's sum, Matemática Pura, Ramanujan theta function, symbols.namesake, Simple (abstract algebra), Identity, symbols, Ramanujan tau function, Ramanujan prime, CIENCIAS NATURALES Y EXACTAS, Mathematics
Abstract

Certain finite families of rational functions have the property that the coefficients of the expansions in power series of their elements are related by simple algebraic expressions. We prove an identity in the spirit of S. Ramanujan using a result of T. N. Sinha. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina

Published
2015

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