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## A complete Vinogradov 3-primes theorem under the Riemann
hypothesis

### J.-M. Deshouillers, G. Effinger, H. te Riele and
D. Zinoviev

**Abstract.**
We outline a proof that if the Generalized Riemann Hypothesis holds,
then every odd number above
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.

*Copyright 1997 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**03** (1997), pp. 99-104
- Publisher Identifier: S 1079-6762(97)00031-0
- 1991
*Mathematics Subject Classification*. Primary 11P32
*Key words and phrases*. Goldbach, Vinogradov, 3-primes
problem, Riemann hypothesis
- Received by the editors February 26, 1997
- Posted on September 17, 1997
- Communicated by Hugh Montgomery
- Comments (When Available)

**J.-M. Deshouillers**

Mathematiques Stochastiques, UMR 9936 CNRS-U.Bordeaux 1,
U.Victor Segalen Bordeaux 2, F33076
Bordeaux Cedex, France

*E-mail address:* `dezou@u-bordeaux2.fr`

**G. Effinger**

Department of Mathematics and Computer Science, Skidmore College,
Saratoga Springs, NY 12866

*E-mail address:* `effinger@skidmore.edu`

**H. te Riele**

Centre for Mathematics and Computer Science, P.O. Box 4079,
1009 AB Amsterdam, The Netherlands

*E-mail address:* `herman.te.riele@cwi.nl`

**D. Zinoviev**

Memotec Communications, Inc., 600 Rue McCaffrey, Montreal,
QC, H4T1N1, Canada

*E-mail address:* `zinovid@memotec.com`

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