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INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES

Part of: Forms and linear algebraic groups Sequences and sets

Published online by Cambridge University Press:  14 August 2019

Alexander Kalmynin
Alexander Kalmynin*
Affiliation:
Mathematics Department, International Laboratory of Mirror Symmetry and Automorphic Forms, National Research University Higher School of Economics, Usacheva 6, Moscow 119048, Russia email alkalb1995cd@mail.ru
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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 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 $\unicode[STIX]{x1D6FE}\leqslant 2$.

MSC classification

Primary: 11E25: Sums of squares and representations by other particular quadratic forms
Secondary: 11B05: Density, gaps, topology
Type
Research Article
Information
Mathematika , Volume 65 , Issue 4 , 2019 , pp. 1018 - 1032
Copyright
Copyright © University College London 2019 

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