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math.NT2026
Versions of Andrews-Gordon Identities Revisited
Alexander Berkovich, Aritram Dhar
In this paper, we revisit the work of Berkovich and Paule on variants of the Andrews-Gordon identities. We find a generalization of their principal polynomial identity and, as a co…
math.NT2025
Further Applications of Cubic -Binomial Transformations
Alexander Berkovich, Aritram Dhar
Consider \begin{align*} G(N,M;α,β,K,q) = \sum\limits_{j\in\mathbb{Z}}(-1)^jq^{\frac{1}{2}Kj((α+β)j+α-β)}\left[\begin{matrix}M+N\\N-Kj\end{matrix}\right]_{q}. \end{align*} In this p…
math.NT2023
On partitions with bounded largest part and fixed integral GBG-rank modulo primes
Alexander Berkovich, Aritram Dhar
In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo which is a generalization of the well-known BG-rank. In this paper, we use the Lit…