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INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES

  • Alexander Kalmynin (a1)

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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INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES

  • Alexander Kalmynin (a1)

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