Mean representation number of integers as the sum of primes-Reference-Cited by-同舟云学术

Mean representation number of integers as the sum of primes

Published:2010-12 Issue: Volume:200 Page:27-33
ISSN:0027-7630
Container-title:Nagoya Mathematical Journal
language:en
Short-container-title:Nagoya Mathematical Journal

Author:

Bhowmik Gautami,Schlage-Puchta Jan-Christoph

Abstract

AbstractAssuming 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. Bhowmik G. and Schlage-Puchta J.-C. , Meromorphic continuation of the Goldbach generating function, to appear in Funct. Approx. Comment. Math., arXiv:1002.4806v1 [math.NT]

2. On the normal density of primes in short intervals, and the difference between consecutive primes;Selberg;Arch. Math. Naturvidenskab,1943

3. A large sieve density estimate near ?=1

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