Analytic continuation of multiple Hurwitz zeta functions

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چکیده

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Analytic continuation of multiple Hurwitz zeta functions

We use a variant of a method of Goncharov, Kontsevich, and Zhao [Go2, Z] to meromorphically continue the multiple Hurwitz zeta function ζd(s; θ) = ∑ 0<n1<···<nd (n1 + θ1) −s1 · · · (nd + θd)d , θk ∈ [0, 1), to C, to locate the hyperplanes containing its possible poles, and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s; θ).

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ژورنال

عنوان ژورنال: Journal of the Mathematical Society of Japan

سال: 2017

ISSN: 0025-5645

DOI: 10.2969/jmsj/06941431