Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.02720 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916824448237568 |
|---|---|
| author | V, Anakha |
| author_facet | V, Anakha |
| contents | Inspired by the recent work by Nadji, Ahmia and Ramírez, we examined the arithmetic properties of $\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular, we establish some congruences modulo k in {4, 8, 6, 12} satisfied by $\bar{B}_{l_1,l_2} (n)$ where $l_1$ and $l_2$ take values as arbitrary powers of 2 and 3. Moreover, we extend certain results proved in [26] and [15] for $l_1$ and $l_2$ with random powers of 2 and 3. Generating functions, dissection formulas, and theta functions are used to prove our main findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Some New Congruences For Biregular Overpartitions V, Anakha Number Theory Inspired by the recent work by Nadji, Ahmia and Ramírez, we examined the arithmetic properties of $\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular, we establish some congruences modulo k in {4, 8, 6, 12} satisfied by $\bar{B}_{l_1,l_2} (n)$ where $l_1$ and $l_2$ take values as arbitrary powers of 2 and 3. Moreover, we extend certain results proved in [26] and [15] for $l_1$ and $l_2$ with random powers of 2 and 3. Generating functions, dissection formulas, and theta functions are used to prove our main findings. |
| title | On Some New Congruences For Biregular Overpartitions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.02720 |