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ON SUMS OF FOUR SQUARES OF PRIMES

  • Angel Kumchev (a1) and Lilu Zhao (a2)

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 $11/32$ .

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