Zeta functions and blow-Nash equivalence

Goulwen Fichou

Displaying similar documents to “Zeta functions and blow-Nash equivalence”

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 $f : (ℝ^{d}, 0) \to (ℝ, 0)$ , we associate zeta functions $Z_{f, +}$ , $Z_{f, -} \in ℤ [[T]]$ , 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...

On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions

Kohji Matsumoto, Takashi Nakamura, Hiroyuki Ochiai, Hirofumi Tsumura (2008)

Acta Arithmetica

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Analytic continuation of multiple zeta-functions and their values at non-positive integers

Shigeki Akiyama, Shigeki Egami, Yoshio Tanigawa (2001)

Acta Arithmetica

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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.

Multiple zeta values for coordinatewise limits at non-positive integers

Yoshitaka Sasaki (2009)

Acta Arithmetica

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Algebraic setup of non-strict multiple zeta values

Shuichi Muneta (2009)

Acta Arithmetica

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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...