Vanishing of the integral of the Hurwitz zeta Function
- 1 February 2002
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 65 (1) , 121-127
- https://doi.org/10.1017/s000497270002013x
Abstract
A proof is given that the improper Riemann integral of ζ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with ℜ(s) < 1. The integral does not exist (as a finite real number) when ℜ(s) ≥ 1.Keywords
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