Vanishing of the integral of the Hurwitz zeta function
نویسنده
چکیده
A number of authors have considered mean values of powers of the modulus of the Hurwitz zeta function ζ(s, a), see [3, 4, 5, 6, 7]. In this paper, the mean of the function itself is considered. First a functional equation relating the Riemann zeta function to sums of the values of the Hurwitz zeta function at rational values of a is derived. This functional equation underlies the vanishing of the integral of the Hurwitz zeta function. Consider the values of the function at negative integers:
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