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SERMON (SouthEast Regional Meeting On Numbers)
April 15-16, 2000
Virginia Tech
Blacksburg, VA, USA |
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Organizers
Ezra Brown, Peter Fletcher
View Abstracts
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Explicit bounds for the Riemann Zeta function
by
Kevin Ford
University of South Carolina
The Vinogradov-Korobov method of exponential sums produces a bound for the Riemann
Zeta function near the line Res = 1 of the form
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|\zeta(s+it)| <= A |t|B(1-s)3/2 log2/3 |t|. |
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We show that one may take B=10.52 and A=100, improving the previous best
published bound of B=21. As an application, we show that the zeta function
is zero-free
in the region
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s >= 1 - 0.0044(log|t|)-2/3 (loglog|t|)-1/3, |t| >= 3. |
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This improves a bound due to Y. Cheng.
Date received: March 3, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caef-02.