A. Kalmynin

activity

20162025

most citedLong nonnegative sums of Legendre symbols

1 citations · 2 across the 12 of their papers we have counts for

collaborators

Showing 2019Show all

3 papers · 1 filter

math.NT2019★ 1 cited

Long nonnegative sums of Legendre symbols

Alexander Kalmynin

For $0 \leq α < 1$ and prime number $p$ let $L (α, p)$ be the sum of the first $[α p]$ values of Legendre symbol modulo $p$ . We study positivity of $L (α, p)$ and prove that for $|α-\frac1…

math.NT2019★ 1 cited

Large gaps between sums of two squares

A. B. Kalmynin, S. V. Konyagin

Let $S = {s_{1} < s_{2} < s_{3} < \dots}$ be the sequence of all natural numbers which can be represented as a sum of two squares of integers. For $X \geq 2$ we denote by $g (X)$ the lar…

math.NT2019

Orthorecursive expansion of unity

Alexander Kalmynin, Petr Kosenko

We study the properties of a sequence cn defined by the recursive relation \[\frac{c_0}{n + 1}+\frac{c_1}{n + 2}+\ldots+\frac{c_n}{2n + 1}=0\] for $n > 1$ and $c_{0} = 1$ . This sequence…