Displaying similar documents to “Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function”

A functional relation for Tornheim's double zeta functions

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...

Universality results on Hurwitz zeta-functions

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.

Small values of the Riemann zeta function on the critical line

Justas Kalpokas, Paulius Šarka (2015)

Acta Arithmetica

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We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.