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Vanishing of the integral of the Hurwitz zeta Function

Published online by Cambridge University Press:  17 April 2009

Kevin A. Broughan
Kevin A. Broughan
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand e-mail: kab@waikato.ac.nz
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 121 - 127
Copyright
Copyright © Australian Mathematical Society 2002

References

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