Real zeros of Hurwitz–Lerch zeta and Hurwitz–Lerch type of Euler–Zagier double zeta functions
نویسندگان
چکیده
منابع مشابه
Real zeros of Dedekind zeta functions of real quadratic fields
Let χ be a primitive, real and even Dirichlet character with conductor q, and let s be a positive real number. An old result of H. Davenport is that the cycle sums Sν(s, χ) = ∑(ν+1)q−1 n=νq+1 χ(n) ns , ν = 0, 1, 2, . . . , are all positive at s = 1, and this has the immediate important consequence of the positivity of L(1, χ). We extend Davenport’s idea to show that in fact for ν ≥ 1, Sν(s, χ) ...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2015
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004115000547