Congruences for the coefficients of the Gordon and McIntosh mock theta function $ξ(q)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866916265283551232 |
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| author | da Silva, Robson Sellers, James A. |
| author_facet | da Silva, Robson Sellers, James A. |
| contents | Recently Gordon and McIntosh introduced the third order mock theta function $ξ(q)$ defined by $$ ξ(q)=1+2\sum_{n=1}^{\infty}\frac{q^{6n^2-6n+1}}{(q;q^6)_{n}(q^5;q^6)_{n}}. $$ Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan--like congruences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_09819 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Congruences for the coefficients of the Gordon and McIntosh mock theta function $ξ(q)$ da Silva, Robson Sellers, James A. Number Theory Combinatorics 11P83, 05A17 Recently Gordon and McIntosh introduced the third order mock theta function $ξ(q)$ defined by $$ ξ(q)=1+2\sum_{n=1}^{\infty}\frac{q^{6n^2-6n+1}}{(q;q^6)_{n}(q^5;q^6)_{n}}. $$ Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan--like congruences. |
| title | Congruences for the coefficients of the Gordon and McIntosh mock theta function $ξ(q)$ |
| topic | Number Theory Combinatorics 11P83, 05A17 |
| url | https://arxiv.org/abs/2007.09819 |