The distribution of zeros of Epstein zeta functions over GLₙ
Riad Masri (2007)
Acta Arithmetica
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Riad Masri (2007)
Acta Arithmetica
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Tsz Ho Chan (2004)
Acta Arithmetica
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D. Ruelle (1975)
Publications mathématiques et informatique de Rennes
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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...
Miki Hirano (1997)
Manuscripta mathematica
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Shuichi Muneta (2009)
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.
Kui Liu (2014)
Acta Arithmetica
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S.M. Gonek, J.B. Conrey, A. Ghosh (1986)
Inventiones mathematicae
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Laurinčikas, A. (2005)
Journal of Mathematical Sciences (New York)
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P.X. Gallagher (1985)
Journal für die reine und angewandte Mathematik
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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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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...
Takashi Nakamura (2006)
Acta Arithmetica
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Shaoji Feng (2005)
Acta Arithmetica
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H. M. Bui, Brian Conrey, Matthew P. Young (2011)
Acta Arithmetica
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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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Habiba Kadiri (2013)
Acta Arithmetica
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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.