On p-adic modular forms and the Bloch-Okounkov theorem

Autor:	Griffin, Michael, Jameson, Marie, Trebat-Leder, Sarah
Rok vydání:	2015
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	Bloch-Okounkov studied certain functions on partitions $f$ called shifted symmetric polynomials. They showed that certain $q$-series arising from these functions (the so-called \emph{$q$-brackets} $\left_q$) are quasimodular forms. We revisit a family of such functions, denoted $Q_k$, and study the $p$-adic properties of their $q$-brackets. To do this, we define regularized versions $Q_k^{(p)}$ for primes $p.$ We also use Jacobi forms to show that the $\left_q$ are quasimodular and find explicit expressions for them in terms of the $\left_q$. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1509.07161 Zobrazit plný text záznamu View this record from Arxiv