The zeta function and discriminant of a division algebra

K. Ramanathan

Displaying similar documents to “The zeta function and discriminant of a division algebra”

Zeta functions of quadratic forms

K. Ramanathan (1961)

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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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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Zeta functions and Eichler integrals

Larry Goldstein (1980)

Acta Arithmetica

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Note on an index formula of elliptic units in a ring class field

Heima Hayashi (1985)

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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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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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.