On multiple Hurwitz zeta-function values at rational arguments
نویسندگان
چکیده
منابع مشابه
Values 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...
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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.
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Throughout this paper, we always make use of the following notation: N = {1, 2, 3, . . .} denotes the set of natural numbers, N0 = {0, 1, 2, 3, . . .} denotes the set of nonnegative integers, Z−0 = {0,−1,−2,−3, . . .} denotes the set of nonpositive integers, Z denotes the set of integers, R denotes the set of real numbers, C denotes the set of complex numbers. The generalized Bernoulli polynomi...
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We investigate a few types of generalizations of the Hurwitz zeta function, written Z(s, a) in this abstract, where s is a complex variable and a is a parameter in the domain that depends on the type. In the easiest case we take a ∈ R, and one of our main results is that Z(−m, a) is a constant times Em(a) for 0 ≤ m ∈ Z, where Em is the generalized Euler polynomial of degree n. In another case, ...
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Let ζ(s1, s2, · · · , sk;α) be the multiple Hurwitz zeta function. Given two positive integers k and n with k 6 n, let E(2n, k;α) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. In this note we present some generating series for the numbers E(2n, k;α).
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2003
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa107-1-5