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Linear equations in primes

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  26 February 2010

Antal Balog
Antal Balog
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, PO Box 127, Budapest, 1368Hungary.
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Extract

§1. Introduction. The literature on solving a system of linear equations in primes is quite limited, although the multi-dimensional Hardy-Littlewood method certainly provides an approach to this problem. The Goldbach- Vinogradov theorem and van der Corput's proof of the existence of infinitely many three term arithmetic progressions in primes are two particular results in the special case of only one equation. Recently Liu and Tsang [4] studied this case in full generality and obtained a result with excellent uniformity in the coefficients. Almost no other general result has appeared so far, due probably to the fact that such a theorem is clumsy to state.

MSC classification

Secondary: 11P32: Goldbach-type theorems; other additive questions involving primes
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 367 - 378
Copyright
Copyright © University College London 1992

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References

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