Sums of Three or More Primes

Authors:
J. B. Friedlander and D. A. Goldston

Journal:
Trans. Amer. Math. Soc. **349** (1997), 287-310

MSC (1991):
Primary 11P32

DOI:
https://doi.org/10.1090/S0002-9947-97-01652-8

MathSciNet review:
1357393

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Abstract: It has long been known that, under the assumption of the Riemann Hypothesis, one can give upper and lower bounds for the error in the Prime Number Theorem, such bounds being within a factor of of each other and this fact being equivalent to the Riemann Hypothesis. In this paper we show that, provided ``Riemann Hypothesis'' is replaced by ``Generalized Riemann Hypothesis'', results of similar (often greater) precision hold in the case of the corresponding formula for the representation of an integer as the sum of primes for , and, in a mean square sense, for . We also sharpen, in most cases to best possible form, the original estimates of Hardy and Littlewood which were based on the assumption of a ``Quasi-Riemann Hypothesis''. We incidentally give a slight sharpening to a well-known exponential sum estimate of Vinogradov-Vaughan.

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Additional Information

**J. B. Friedlander**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada

Email:
frdlndr@math.toronto.edu

**D. A. Goldston**

Affiliation:
Department of Mathematics and Computer Science, San Jose State University, San Jose, California 95192

Email:
goldston@sjsumcs.sjsu.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01652-8

Received by editor(s):
April 29, 1994

Received by editor(s) in revised form:
September 22, 1995

Additional Notes:
Research of the first author supported in part by NSERC Grant A5123 and NSF Grant DMS8505550.

Research of the second author supported in part by NSF Grant DMS9205533.

Article copyright:
© Copyright 1997
American Mathematical Society