Broughan, Kevin A.2009-02-222009-02-222002Broughan, K.A. (2002). Vanishing of the integral of the Hurwitz zeta function. Bulletin of the Australian Mathematical Society, 65, 121-127.https://hdl.handle.net/10289/2037A proof is given that the improper Riemann integral of δ(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.application/pdfenThis is an author’s final version of an article published in the journal: Bulletin of the Australian Mathematical Society. © 2002 Australian Mathematical Society. Used with permission.Hurwitz zeta functionfunctional equationimproper Riemann integralJournal Article10.1017/S000497270002013X