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On sums of squares of primes

Published online by Cambridge University Press:  11 January 2006

GLYN HARMAN  and
ANGEL V. KUMCHEV
GLYN HARMAN
Affiliation:
Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX. e-mail: G.Harman@rhul.ac.uk
ANGEL V. KUMCHEV
Affiliation:
Mathematics Dept., Towson University, 8000 York Road, Towson MD 21252, USA. e-mail: akumchev@towson.edu
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Abstract

In this paper we consider the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. Using new exponential sums in tandem with a sieve method we are able to provide stronger “minor arc” estimates than previous authors, thereby improving the saving obtained in the exponent by a factor 8/7.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 140 , Issue 1 , January 2006 , pp. 1 - 13
Copyright
2006 Cambridge Philosophical Society

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