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

14 papers

math.NT2025

On additive irreducibility of multiplicative subgroups

Alexander Kalmynin

In this paper, we employ a version of Stepanov's method, developed by Hanson and Petridis, to prove several results on additive irreducibility of multiplicative subgroups in finite…

math.NT2024

Omega theorem for fractional sigma function

Yuan Qiu, Alexander B. Kalmynin

The research in the subfield of analytic number theory around error term of summation of sigma functions possesses a history which can be dated back to the mid-19th century when Di…

math.NT2024

Sums of squares and sequences of modular forms

Alexander Kalmynin

Let $h_{n} (v)$ be the sequence of rational functions with $\frac{h _{n} ( v )}{v} - n h_{n} (v) + (n - 1) h_{n - 1} (v) - v h_{n - 1}^{'} (v) + \frac{v ( v ( v h _{n - 1} ( v ) ) ^{'} ) ^{'}}{4} = 0$ for $n > 0$ and $h_{0} (v) = 1$ . We pro…

math.NT2023

Large gaps between sums of two squareful numbers

Alexander Kalmynin, Sergei Konyagin

Let $M (x)$ be the length of the largest subinterval of $[1, x]$ which does not contain any sums of two squareful numbers. We prove a lower bound \[ M(x)\gg \frac{\ln x}{(\ln\ln x)^2…

math.NT2023

A polynomial analogue of Jacobsthal function

Alexander Kalmynin, Sergei Konyagin

For a polynomial $f (x) \in Z [x]$ we study an analogue of Jacobsthal function, defined by the formula \[ j_f(N)=\max_{m}\{\text{For some } x\in \mathbb N \text{ the inequalit…

math.NT2021

Quadratic characters with positive partial sums

Alexander Kalmynin

Let $L^{+}$ be the set of all primes $p$ for which the sums of $(\frac{n}{p})$ over the interval $[1, N]$ are non-negative for all $N$ . We prove that the estimate…