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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A. Terras (1976)
Acta Arithmetica
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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 .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.
Paul Bateman, E. Grosswald (1964)
Acta Arithmetica
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Janusz Szmidt (1983)
Acta Arithmetica
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M. Forti, Carlo Viola (1973)
Acta Arithmetica
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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 and , 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 , , , and is irrational.
E. Bombieri, H. Iwaniec (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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