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ISSN 1079-6762

 

A complete Vinogradov 3-primes theorem under the Riemann hypothesis


Authors: J.-M. Deshouillers, G. Effinger, H. te Riele and D. Zinoviev
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 99-104
MSC (1991): Primary 11P32
Published electronically: September 17, 1997
MathSciNet review: 1469323
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Abstract: We outline a proof that if the Generalized Riemann Hypothesis holds, then every odd number above $5$ is a sum of three prime numbers. The proof involves an asymptotic theorem covering all but a finite number of cases, an intermediate lemma, and an extensive computation.


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Additional Information

J.-M. Deshouillers
Affiliation: Mathematiques Stochastiques, UMR 9936 CNRS-U.Bordeaux 1, U.Victor Segalen Bordeaux 2, F33076 Bordeaux Cedex, France
Email: dezou@u-bordeaux2.fr

G. Effinger
Affiliation: Department of Mathematics and Computer Science, Skidmore College, Saratoga Springs, NY 12866
Email: effinger@skidmore.edu

H. te Riele
Affiliation: Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands
Email: herman.te.riele@cwi.nl

D. Zinoviev
Affiliation: Memotec Communications, Inc., 600 Rue McCaffrey, Montreal, QC, H4T1N1, Canada
Email: zinovid@memotec.com

DOI: http://dx.doi.org/10.1090/S1079-6762-97-00031-0
PII: S 1079-6762(97)00031-0
Keywords: Goldbach, Vinogradov, 3-primes problem, Riemann hypothesis
Received by editor(s): February 26, 1997
Published electronically: September 17, 1997
Communicated by: Hugh Montgomery
Article copyright: © Copyright 1997 American Mathematical Society