Some formulas for the Riemann zeta function at odd integer argument resulting from Fourier expansions of the Epstein zeta function

A. Terras

Displaying similar documents to “Some formulas for the Riemann zeta function at odd integer argument resulting from Fourier expansions of the Epstein zeta function”

The Fourier expansion of Epstein's zeta function for totally real algebraic number fields and some consequences for Dedekind's zeta function

A. Terras (1976)

Acta Arithmetica

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Bounds for double zeta-functions

Isao Kiuchi, Yoshio Tanigawa (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region $0 \leq ℜ s_{j} < 1 (j = 1, 2)$ .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.

On Epstein's zeta function

Paul Bateman, E. Grosswald (1964)

Acta Arithmetica

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The Selberg trace formula for the Picard group SL(2, Z[i])

Janusz Szmidt (1983)

Acta Arithmetica

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Density estimates for the zeros of L-functions

M. Forti, Carlo Viola (1973)

Acta Arithmetica

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Arithmetic of linear forms involving odd zeta values

Wadim Zudilin (2004)

Journal de Théorie des Nombres de Bordeaux

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A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $ζ (2)$ and $ζ (3)$ , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers $ζ (5)$ , $ζ (7)$ , $ζ (9)$ , and $ζ (11)$ is irrational.

On the order of $ζ (\frac{1}{2} + i t)$

E. Bombieri, H. Iwaniec (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Displaying similar documents to “Some formulas for the Riemann zeta function at odd integer argument resulting from Fourier expansions of the Epstein zeta function”

The Fourier expansion of Epstein's zeta function for totally real algebraic number fields and some consequences for Dedekind's zeta function

Bounds for double zeta-functions

On Epstein's zeta function

The Selberg trace formula for the Picard group SL(2, Z[i])

Density estimates for the zeros of L-functions

Arithmetic of linear forms involving odd zeta values

On the order of ζ ( 1 2 + i t )

On the order of $ζ (\frac{1}{2} + i t)$