On Ramanujan's formula for values of Riemann zeta-function at positive odd integers

Koji Katayama

Displaying similar documents to “On Ramanujan's formula for values of Riemann zeta-function at positive odd integers”

An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions.

Masanori Katsurada (1997)

Collectanea Mathematica

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We shall establish full asymptotic expansions for the mean squares of Lerch zeta-functions, based on F. V. Atkinson's device. Mellin-Barnes' type integral expression for an infinite double sum will play a central role in the derivation of our main formulae.

On Epstein's zeta function

Paul Bateman, E. Grosswald (1964)

Acta Arithmetica

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Well-poised hypergeometric service for diophantine problems of zeta values

Wadim Zudilin (2003)

Journal de théorie des nombres de Bordeaux

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It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studying arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in $1$ and $ζ (4) = π^{4} / 90$ yielding a conditional upper bound for the irrationality measure of $ζ (4)$ ; (2) a second-order Apéry-like recursion for $ζ (4)$ and some low-order recursions for linear forms in odd zeta values; (3) a rich permutation group...

On an asymptotic formula of Ramanujan for a certain theta-type series

Masanori Katsurada (2001)

Acta Arithmetica

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A generalized Euler-Maclaurin formula for the Hurwitz zeta function

Eugenio P. Balanzario (2006)

Mathematica Slovaca

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Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function

Masanori Katsurada (2003)

Acta Arithmetica

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A relation between the Riemann zeta-function and the hyperbolic laplacian

Yoichi Motohashi (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On multiple analogues of Ramanujan’s formulas for certain Dirichlet series

Hirofumi Tsumura (2008)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we prove multiple analogues of famous Ramanujan’s formulas for certain Dirichlet series which were introduced in his well-known notebooks. Furthermore, we prove some multiple versions of analogous formulas of Ramanujan which were given by Berndt and so on.