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Article

Intervals between consecutive numbers which are sums of two squares

Mathematika. 2019. Vol. 65. No. 4. P. 1018-1032.

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 mean value. This bound provides estimates for the γ-th moments of gaps for all γ\leq 2.