### The meromorphic continuation of a zeta function of Weil and Igusa Type.

D. Meuser (1986)

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D. Meuser (1986)

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M. Zakrzewski (2012)

Banach Center Publications

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This is an expository article, based on the talk with the same title, given at the 2011 FASDE II Conference in Będlewo, Poland. In the introduction we define Multiple Zeta Values and certain historical remarks are given. Then we present several results on Multiple Zeta Values and, in particular, we introduce certain meromorphic differential equations associated to their generating function. Finally, we make some conclusive remarks on generalisations of Multiple Zeta Values as well as...

Mariusz Wodzicki (1982)

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Michał Zakrzewski, Henryk Żołądek (2010)

Fundamenta Mathematicae

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Certain generating fuctions for multiple zeta values are expressed as values at some point of solutions of linear meromorphic differential equations. We apply asymptotic expansion methods (like the WKB method and the Stokes operators) to solutions of these equations. In this way we give a new proof of the Euler formula ζ(2) = π²/6. In further papers we plan to apply this method to study some third order hypergeometric equation related to ζ(3).

Goro Shimura (1995)

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Robert Speiser (1980/81)

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I. Lahiri (1989)

Matematički Vesnik

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S. K. Bajpai, T. J. S. Mehrok (1975)

Annales Polonici Mathematici

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David Ruelle (1976)

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W. K. Hayman (1981)

Annales Polonici Mathematici

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P. K. Jain, P. K. Kamthan (1972)

Annales Polonici Mathematici

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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1976)

Annales Polonici Mathematici

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J.V. Armitage (1971/72)

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