Explicit Formulas and Asymptotic Expansions for Certain Mean Square of Hurwitz Zeta-Functions.
M. Katsurada, K. Matsumoto (1996)
Mathematica Scandinavica
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M. Katsurada, K. Matsumoto (1996)
Mathematica Scandinavica
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Masanori Katsurada (2003)
Acta Arithmetica
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Masanori Katsurada (2001)
Acta Arithmetica
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K. Bartz (1991)
Acta Arithmetica
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K. Bartz (1991)
Acta Arithmetica
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Masanori Katsurada (2012)
Acta Arithmetica
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Kazuhiro Onodera (2014)
Acta Arithmetica
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We generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results on the behavior of a certain Witten's zeta...
Shuichi Muneta (2009)
Acta Arithmetica
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M. Zakrzewski (2012)
Banach Center Publications
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This is an expository article, based on the talk with the same title, given at the 2011 FASDE II Conference in Będlewo, Poland. In the introduction we define Multiple Zeta Values and certain historical remarks are given. Then we present several results on Multiple Zeta Values and, in particular, we introduce certain meromorphic differential equations associated to their generating function. Finally, we make some conclusive remarks on generalisations of Multiple Zeta Values as well as...
Kui Liu (2014)
Acta Arithmetica
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Antanas Laurinčikas, Renata Macaitienė (2016)
Banach Center Publications
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In the paper, we give a survey of the results on the approximation of analytic functions by shifts of Hurwitz zeta-functions. Theorems of such a kind are called universality theorems. Continuous, discrete and joint universality theorems of Hurwitz zeta-functions are discussed.
Masanori Katsurada (1997)
Publications de l'Institut Mathématique
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Laurinčikas, A. (2005)
Journal of Mathematical Sciences (New York)
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Kim, T., Jang, L.C., Rim, S.H. (2004)
International Journal of Mathematics and Mathematical Sciences
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John M. Franks (1975)
Publications mathématiques et informatique de Rennes
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Yoshitaka Sasaki (2009)
Acta Arithmetica
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Sanoli Gun, M. Ram Murty, Purusottam Rath (2012)
Acta Arithmetica
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Michał Zakrzewski, Henryk Żołądek (2010)
Fundamenta Mathematicae
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Certain generating fuctions for multiple zeta values are expressed as values at some point of solutions of linear meromorphic differential equations. We apply asymptotic expansion methods (like the WKB method and the Stokes operators) to solutions of these equations. In this way we give a new proof of the Euler formula ζ(2) = π²/6. In further papers we plan to apply this method to study some third order hypergeometric equation related to ζ(3).