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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Riemann hypothesis, simple zeros
and the asymptotic convergence degree
of improper Riemann sums


Author: Jonathan Sondow
Journal: Proc. Amer. Math. Soc. 126 (1998), 1311-1314
MSC (1991): Primary 11M26; Secondary 40A05
MathSciNet review: 1469435
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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the nonreal zeros of the Riemann zeta function and their multiplicities, using the ``asymptotic convergence degree'' of ``improper Riemann sums'' for elementary improper integrals. The Riemann Hypothesis and the conjecture that all the zeros are simple then have elementary formulations.


References [Enhancements On Off] (What's this?)

  • 1. H. M. Edwards, Riemann’s zeta function, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Pure and Applied Mathematics, Vol. 58. MR 0466039 (57 #5922)

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Additional Information

Jonathan Sondow
Affiliation: 209 West 97th Street, New York, New York 10025

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04607-3
PII: S 0002-9939(98)04607-3
Received by editor(s): October 28, 1996
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1998 American Mathematical Society