INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES
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DOI: 10.1112/s0025579319000299
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… read more here.
Keywords: numbers sums; sums two; intervals consecutive; consecutive numbers ... See more keywords
Sums of one prime power and two squares of primes in short intervals
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DOI: 10.1216/rmj.2021.51.213
Abstract: Let k≥1 be an integer. We prove that a suitable asymptotic formula for the average number of representations of integers n=p1k+p22+p32, where p1, p2, p3 are prime numbers, holds in intervals shorter than the ones… read more here.
Keywords: squares primes; prime power; sums one; two squares ... See more keywords
Difference Equation for Functions Analytic Outside Two Squares
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DOI: 10.3103/s1066369x18060014
Abstract: We consider a totality of two squares built on primitive periods 1 and i and “sufficiently close to each other“. In a vicinity of this set we investigate four-element difference equation with constant coefficients, whose… read more here.
Keywords: analytic outside; difference equation; two squares; equation ... See more keywords