منابع مشابه
On the Hurwitz function for rational arguments
Using functional properties of the Hurwitz zeta function and symbolic derivatives of the trigonometric functions, the function ζ(2n + 1, p/q) is expressed in several ways in terms of other mathematical functions and numbers, including in particular the Glaisher numbers. 2000 Mathematics Subject Classification. Primary 11M35, 33B99. Secondary 11B75, 33E20.
متن کاملValues of the Legendre chi and Hurwitz zeta functions at rational arguments
We show that the Hurwitz zeta function, ζ(ν, a), and the Legendre chi function, χν(z), defined by ζ(ν, a) = ∞ ∑ k=0 1 (k + a)ν , 0 < a ≤ 1, Re ν > 1, and χν(z) = ∞ ∑ k=0 z2k+1 (2k + 1)ν , |z| ≤ 1, Re ν > 1 with ν = 2, 3, 4, . . . , respectively, form a discrete Fourier transform pair. Many formulae involving the values of these functions at rational arguments, most of them unknown, are obtained...
متن کاملCounting Ramified Coverings and Intersection Theory on Spaces of Rational Functions I (cohomology of Hurwitz Spaces)
The Hurwitz space is a compactification of the space of rational functions of a given degree. The Lyashko–Looijenga map assigns to a rational function the set of its critical values. It is known that the number of ramified coverings of CP by CP with prescribed ramification points and ramification types is related to the degree of the Lyashko–Looijenga map on various strata of the Hurwitz space....
متن کاملGenerating Functions for Hurwitz-Hodge Integrals
In this paper we describe explicit generating functions for a large class of Hurwitz-Hodge integrals. These are integrals of tautological classes on moduli spaces of admissible covers, a (stackily) smooth compactification of the Hurwitz schemes. Admissible covers and their tautological classes are interesting mathematical objects on their own, but recently they have proved to be a useful tool f...
متن کاملAnalytic 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: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.03.062