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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.20025 |
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| _version_ | 1866914344251424768 |
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| author | Baruah, Nayandeep Deka Gogoi, Pankaj |
| author_facet | Baruah, Nayandeep Deka Gogoi, Pankaj |
| contents | 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 $DSOME(n)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20025 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arithmetic properties of DSOME function Baruah, Nayandeep Deka Gogoi, Pankaj Number Theory 11P83, 05A17 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 $DSOME(n)$. |
| title | Arithmetic properties of DSOME function |
| topic | Number Theory 11P83, 05A17 |
| url | https://arxiv.org/abs/2602.20025 |