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arXiv · 2602.20025

Arithmetic properties of DSOME function

Nayandeep Deka Baruah·Pankaj Gogoi
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Abstract

Recently, Andrews and Ghosh Dastidar (Ramanujan J. \textbf{69}, Art. No. 26, 2026) studied two interesting functions $SOME(n)$ and $DSOME(n)$, where $SOME(n)$ is the sum of all the odd parts in the partitions of $n$ minus the sum of all even parts and $DSOME(n)$ is the sum of all the odd parts in the partitions of $n$ into distinct parts minus sum of all the even parts. They expressed the generating functions of $SOME(n)$ and $DSOME(n)$ in terms of $q$-series and found several interesting congruences modulo 4 and 5. In this paper, we express the generating function of $DSOME(n)$ in a closed form, which allows us to find some new congruences and internal congruences modulo 4 and 8 for $DSOME(n)$.

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Nayandeep Deka Baruah, Pankaj Gogoi. 2026-02-20. Arithmetic properties of DSOME function. https://arxiv.org/abs/2602.20025

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