Displaying similar documents to “Analytic continuation of multiple zeta-functions and their values at non-positive integers”

On the singularities of multiple L-functions

Alexandru Zaharescu, Mohammad Zaki (2010)

Open Mathematics

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We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].

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.

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...

Motivic-type invariants of blow-analytic equivalence

Satoshi Koike, Adam Parusiński (2003)

Annales de l'Institut Fourier

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To a given analytic function germ f : ( ℝ d , 0 ) → ( ℝ , 0 ) , we associate zeta functions Z f , + , Z f , - ∈ ℤ [ [ T ] ] , defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies as well the blow-analytic...