A. Kalmynin

collaborators

3 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…