Ajit Singh

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math.NT2024

Recursive Formulas for MacMahon and Ramanujan $q$ -series

Tewodros Amdeberhan, Rupam Barman, Ajit Singh

In the present work, we extend current research in a nearly-forgotten but newly revived topic, initiated by P. A. MacMahon, on a generalized notion which relates the divisor sums t…

math.NT2024

Certain infinite products in terms of MacMahon type series

Seokho Jin, Badri Vishal Pandey, Ajit Singh

Recently, Ono and the third author discovered that the reciprocals of the theta series $(q; q)_{\infty}^{3}$ and $(q^{2}; q^{2})_{\infty} (q; q^{2})_{\infty}^{2}$ have infinitely many closed formulas…

math.NT2023

Parity distribution and divisibility of Mex-related partition functions

Subhrajyoti Bhattacharyya, Rupam Barman, Ajit Singh +1

Andrews and Newman introduced the mex-function $mex_{A, a} (λ)$ for an integer partition $λ$ of a positive integer $n$ as the smallest positive integer congruent to $a$ modulo…

math.NT2023

Certain Diophantine equations and new parity results for $21$ -regular partitions

Ajit Singh, Gurinder Singh, Rupam Barman

For a positive integer $t \geq 2$ , let $b_{t} (n)$ denote the number of $t$ -regular partitions of a nonnegative integer $n$ . In a recent paper, Keith and Zanello investigated the par…

math.NT2022

Arithmetic properties of certain $t$ -regular partitions

Rupam Barman, Ajit Singh, Gurinder Singh

For a positive integer $t \geq 2$ , let $b_{t} (n)$ denote the number of $t$ -regular partitions of a nonnegative integer $n$ . Motivated by some recent conjectures of Keith and Zanello…

Recursive Formulas for MacMahon and Ramanujan q-series

Certain infinite products in terms of MacMahon type series

Parity distribution and divisibility of Mex-related partition functions

Certain Diophantine equations and new parity results for 21-regular partitions

Arithmetic properties of certain t-regular partitions

Recursive Formulas for MacMahon and Ramanujan $q$ -series

Certain Diophantine equations and new parity results for $21$ -regular partitions

Arithmetic properties of certain $t$ -regular partitions