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Sums of Five Almost Equal Prime Squares

Authors:	Claus Bauer

Institution:	(1) Dolby Laboratories, 100 Potrero Avenue, San Francisco, CA, 94103, USA

Abstract:	Let P _i, 1 ≤ i ≤ 5, be prime numbers. It is proved that every integer N that satisfies N ≡ 5(mod24) can be written as $N = p^{2}_{1} + p^{2}_{2} + p^{2}_{3} + p^{2}_{4} + p^{2}_{5} ,{\text{where}}{\left\| {{\sqrt N }5 - p_{i} } \right\|} \leqslant N^{{\frac{1} {2} - \frac{{19}} {{850}} + \in }}$ .

Keywords:	Prime numbers Exponential sums L-functions
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