The Riemann Hypothesis, simple zeros and the asymptotic convergence degree of improper Riemann sums
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- by Jonathan Sondow PDF
- Proc. Amer. Math. Soc. 126 (1998), 1311-1314 Request permission
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
- H. M. Edwards, Riemann’s zeta function, Pure and Applied Mathematics, Vol. 58, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0466039
Additional Information
- Jonathan Sondow
- Affiliation: 209 West 97th Street, New York, New York 10025
- Received by editor(s): October 28, 1996
- Communicated by: Dennis A. Hejhal
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1311-1314
- MSC (1991): Primary 11M26; Secondary 40A05
- DOI: https://doi.org/10.1090/S0002-9939-98-04607-3
- MathSciNet review: 1469435