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ON PAIRS OF GOLDBACH–LINNIK EQUATIONS

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  19 October 2016

YAFANG KONG  and
ZHIXIN LIU
YAFANG KONG
Affiliation:
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, PR China email [email protected]
ZHIXIN LIU*
Affiliation:
Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, PR China email [email protected]
*
✉[email protected]
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Abstract

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In this paper, we show that every pair of large positive even integers can be represented in the form of a pair of Goldbach–Linnik equations, that is, linear equations in two primes and $k$ powers of two. In particular, $k=34$ powers of two suffice, in general, and $k=18$ under the generalised Riemann hypothesis. Our result sharpens the number of powers of two in previous results, which gave $k=62$, in general, and $k=31$ under the generalised Riemann hypothesis.

Keywords

Goldbach–Linnik problemcircle methodpairs of equations

MSC classification

Primary: 11P32: Goldbach-type theorems; other additive questions involving primes
Secondary: 11P05: Waring's problem and variants 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 199 - 208
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11426048 and 11301372), Specialised Research Fund for the Doctoral Program of Higher Education (Grant No. 20130032120073) and Independent Innovation Foundation of Tianjin University (Grant Nos 190-0903061029 and 190-0903062072).

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