Explicit evaluations of quadruple Euler sums
Yao Lin Ong, Minking Eie, Chuan-Sheng Wei (2010)
Acta Arithmetica
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Yao Lin Ong, Minking Eie, Chuan-Sheng Wei (2010)
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...
Kim, T., Jang, L.C., Rim, S.H. (2004)
International Journal of Mathematics and Mathematical Sciences
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Takashi Nakamura (2006)
Acta Arithmetica
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Shuichi Muneta (2009)
Acta Arithmetica
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Boyadzhiev, Khristo N. (2002)
International Journal of Mathematics and Mathematical Sciences
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Muharem Avdispahić, Lejla Smajlović (2008)
Acta Arithmetica
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Zhao, Jianqiang (2010)
Integers
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Yoshitaka Sasaki (2009)
Acta Arithmetica
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Laurinčikas, A. (2005)
Journal of Mathematical Sciences (New York)
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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.
Bao Qin Li, Zhuan Ye (2008)
Acta Arithmetica
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Kui Liu (2014)
Acta Arithmetica
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John M. Franks (1975)
Publications mathématiques et informatique de Rennes
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Sofo, Anthony (2004)
International Journal of Mathematics and Mathematical Sciences
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Takuya Okamoto (2009)
Acta Arithmetica
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Sanoli Gun, M. Ram Murty, Purusottam Rath (2012)
Acta Arithmetica
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M. C. Lettington (2013)
Acta Arithmetica
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We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli...