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INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES
Published online by Cambridge University Press: 14 August 2019
Abstract
In this paper, we improve the moment estimates for the gaps between numbers that can be represented as a sum of two squares of integers. We consider a certain sum of Bessel functions and prove the upper bound for its mean value. This bound provides estimates for the $\unicode[STIX]{x1D6FE}$th moments of gaps for all $\unicode[STIX]{x1D6FE}\leqslant 2$.
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- Research Article
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- Copyright © University College London 2019