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INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES

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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… Click to show full 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 γ-th moments of gaps for all γ ⩽ 2. §

Keywords: numbers sums; sums two; intervals consecutive; consecutive numbers; two squares

Journal Title: Mathematika
Year Published: 2019

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