Zeta functions of quadratic forms

K. Ramanathan

Displaying similar documents to “Zeta functions of quadratic forms”

The Fourier expansion of Epstein's zeta function over an algebraic number field and its consequences for algebraic number theory

A. Terras (1977)

Acta Arithmetica

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On Epstein's zeta function

Paul Bateman, E. Grosswald (1964)

Acta Arithmetica

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The zeta function and discriminant of a division algebra

K. Ramanathan (1959)

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.

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

Janusz Szmidt (1983)

Acta Arithmetica

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

A. Terras (1976)

Acta Arithmetica

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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.