arXiv subjects

Zhumagali Shomanov

Publications and source records attributed to Zhumagali Shomanov.

3 recordsLinked to original sources

arXiv2025

An infinite family of overpartition congruences mod powers of 2

We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's $U_2$ operator, we determine lower bounds on the 2-adic valuations of the coefficients that arise at each step. Our approach yields new modular equations relating the Hauptmoduln $G_2$ on $Γ_0(2)$ and $G_8$ on $Γ_0(8)$, together with explicit $U_2$-action formulas.

math.NT↗

arXiv2025

A simple proof of the Atkin-O'Brien partition congruence conjecture for powers of 13

In 1967, Atkin and O'Brien conjectured congruences for the partition function involving Hecke operators modulo powers of 13. In this paper, we provide a simple proof of this conjecture.

math.NT↗

arXiv2016

Combinatorial Formula for the Partition Function

In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial coefficients.

math.CO↗