An elementary approach to the twin primes problem

Baier, S. (2004) An elementary approach to the twin primes problem. Monatshefte für Mathematik, 143 (4). pp. 269-283. ISSN 0026-9255

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Abstract

Hardy-Littlewood [4] conjectured an asymptotic formula for the number of prime pairs (twin primes) (p, p + 2d) with p + 2d = y, where d ? N is fixed and y ? 8. Up to now, no one has been able to prove this conjecture, but employing Hardy-Littlewood's circle method, Lavrik [5] showed that in a certain sense this formula holds true for almost-all d = y/2. In the present paper, we use a completely different method to prove Lavrik's almost-all result. Our method is based on an elementary approach developed by Pan Chengdong [7] to the twin primes problem. By a slight modification of our method, we get a corresponding almost-all result for the binary Goldbach problem. From this, according to [3], we derive Vinogradov's [8] well-known Three-Primes-Theorem.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Number Theory, Ergodic Theory and Dynamical Systems (former - to 2013) Faculty of Science > Research Groups > Number Theory (former - to 2017)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	Pure Connector
Date Deposited:	07 Sep 2013 05:12
Last Modified:	24 Oct 2022 04:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/43190
DOI:	10.1007/s00605-004-0270-3

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