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ON SUMS OF FOUR SQUARES OF PRIMES

Part of: Multiplicative number theory Additive number theory; partitions Exponential sums and character sums

Published online by Cambridge University Press:  22 January 2016

Angel Kumchev  and
Lilu Zhao
Angel Kumchev
Affiliation:
Department of Mathematics, Towson University, 7800 York Road, Towson, MD 21252, U.S.A. email akumchev@towson.edu
Lilu Zhao
Affiliation:
School of Mathematics, Hefei University of Technology, Hefei 230009, China email zhaolilu@gmail.com
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Abstract

Let $E(N)$ denote the number of positive integers $n\leqslant N$, with $n\equiv 4\;(\text{mod}\;24)$, which cannot be represented as the sum of four squares of primes. We establish that $E(N)\ll N^{11/32}$, thus improving on an earlier result of Harman and the first author, where the exponent $7/20$ appears in place of $11/32$.

MSC classification

Primary: 11P32: Goldbach-type theorems; other additive questions involving primes
Secondary: 11L20: Sums over primes 11N36: Applications of sieve methods 11P05: Waring's problem and variants 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Mathematika , Volume 62 , Issue 2 , 2016 , pp. 348 - 361
Copyright
Copyright Š University College London 2016 

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