On the mean value of a kind of zeta functions
Kui Liu (2014)
Acta Arithmetica
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Kui Liu (2014)
Acta Arithmetica
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Shuichi Muneta (2009)
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...
Yoshitaka Sasaki (2009)
Acta Arithmetica
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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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Sanoli Gun, M. Ram Murty, Purusottam Rath (2012)
Acta Arithmetica
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Kohji Matsumoto, Takashi Nakamura, Hiroyuki Ochiai, Hirofumi Tsumura (2008)
Acta Arithmetica
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Đurđe Cvijović, Jacek Klinowski (2000)
Matematički Vesnik
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Takashi Nakamura (2006)
Acta Arithmetica
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Johan Andersson (1992)
Mathematica Scandinavica
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S. Kanemitsu, Y. Tanigawa, M. Yoshimoto (2003)
Acta Arithmetica
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Takuya Okamoto (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...
Zudilin, W. (2005)
Journal of Mathematical Sciences (New York)
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Masanori Katsurada (2001)
Acta Arithmetica
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Norman Levinson (1972)
Acta Arithmetica
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