https://scholars.lib.ntu.edu.tw/handle/123456789/626606
標題: | The smallest parts function associated with omega(q) | 作者: | Wang, LQ YI-FAN YANG |
關鍵字: | Partitions; mock theta function; smallest parts functions; congruences modulo powers of 5; Eisenstein series; CONGRUENCES; PARTITIONS | 公開日期: | 1-十一月-2022 | 出版社: | WORLD SCIENTIFIC PUBL CO PTE LTD | 卷: | 18 | 期: | 10 | 起(迄)頁: | 2279 | 來源出版物: | INTERNATIONAL JOURNAL OF NUMBER THEORY | 摘要: | We establish two families of congruences modulo powers of 5 for the Fourier coefficients of (2E2(2τ) - E2(τ))η(2τ)-1, where E2(τ) is the weight 2 Eisenstein series and η(τ) is the Dedekind eta function. This allows us to prove similar congruences for two smallest parts functions. The first function is sptω(n), which was introduced by Andrews, Dixit and Yee and is associated with Ramanujan/Watson's third-order mock theta function ω(q). The second one is sptC5(n), which appeared in the work of Garvan and Jennings-Shaffer. Moreover, we confirm two conjectural congruences of Wang. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/626606 | ISSN: | 1793-0421 | DOI: | 10.1142/S1793042122501160 |
顯示於: | 數學系 |
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