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Mean representation number of integers as the sum of primes

Published online by Cambridge University Press:  11 January 2016

Gautami Bhowmik  and
Jan-Christoph Schlage-Puchta
Gautami Bhowmik
Affiliation:
Université de Lille 1, Laboratoire Paul Painlevé UMR CNRS 8524, 59655 Villeneuve d’Ascq Cedex, France, bhowmik@math.univ-lille1.fr
Jan-Christoph Schlage-Puchta
Affiliation:
University of Gent, Department of Pure Mathematics and Computer Algebra, 9000 Gent, Belgium, jcsp@cage.ugent.be
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Abstract

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Assuming the Riemann hypothesis, we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Ω-term, we show that our result is essentially the best possible.

Keywords

11P3211P55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 200 , December 2010 , pp. 27 - 33
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

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