A -analog of Euler's decomposition formula for the double zeta function.
Bradley, David M. (2005)
International Journal of Mathematics and Mathematical Sciences
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Bradley, David M. (2005)
International Journal of Mathematics and Mathematical Sciences
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Boyadzhiev, Khristo N. (2002)
International Journal of Mathematics and Mathematical Sciences
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Hirofumi Tsumura (2004)
Acta Arithmetica
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Bailey, David H., Borwein, Jonathan M., Girgensohn, Roland (1994)
Experimental Mathematics
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Bao Qin Li, Zhuan Ye (2008)
Acta Arithmetica
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Muharem Avdispahić, Lejla Smajlović (2008)
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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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...
Borwein, Jonathan Michael, Broadhurst, David J., Kamnitzer, Joel (2001)
Experimental Mathematics
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Kazufumi Kimoto, Nobushige Kurokawa, Sho Matsumoto, Masato Wakayama (2005)
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.
Laurinčikas, A. (2005)
Journal of Mathematical Sciences (New York)
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Yoshitaka Sasaki (2009)
Acta Arithmetica
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Zhao, Jianqiang (2010)
Integers
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Masanori Katsurada (2003)
Acta Arithmetica
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