On sums of squares of primes II

Details On sums of squares of primes II On sums of squares of primes II

2009-02-24

arxiv.org/abs/0902.4190v1

J. Number Theory 130 (2010), 1969-2002

Mathematics

Number Theory

30 pages

Scientific paper

In this paper we continue our study, begun in part I, of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious oversight in our first paper, but make further progress on the exponential sums estimates needed, together with an embellishment of the previous sieve technique employed. This leads to an improvement in our bounds for the maximal size of the exceptional sets.

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