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arXiv · 1706.07380

Intervals between numbers that are sums of two squares

Alexander Kalmynin
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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 certain sum of Bessel functions and prove the upper bound for its weighted mean value. This bound provides estimates for the $\gamma$-th moments of gaps for all $\gamma\leq 2$.

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Alexander Kalmynin. 2017-06-22. Intervals between numbers that are sums of two squares. https://doi.org/10.1112/s0025579319000299

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