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- W2968152687 abstract "The coefficients of the generating function $(q;q)^alpha_infty$ produce $p_alpha(n)$ for $alpha in mathbb{Q}$. In particular, when $alpha = -1$, the partition function is obtained. Recently, Chan and Wang identified and proved congruences of the form $p_{frac{a}{b}}(ell n + c)equiv 0 pmod{ell}$ where $ell$ is a prime such that $ell mid a -db$ for $d in {4, 6, 8, 10, 14, 26}$. Expanding upon their work, we use the representation of powers of the Dedekind-eta functions in linear sums of Hecke eigenforms and their lacunarity to raise the power of the modulus to higher powers of $ell$. In addition, we generate congruences for when $d=2$ employing Hecke algebra." @default.
- W2968152687 created "2019-08-22" @default.
- W2968152687 creator A5042262350 @default.
- W2968152687 date "2019-08-11" @default.
- W2968152687 modified "2023-09-27" @default.
- W2968152687 title "Congruences in fractional partition functions" @default.
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