Marie Jameson

Affiliation: University of Tennessee


Title Of Talk: On $p$-adic modular forms and the Bloch-Okounkov theorem

Abstract: 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 $q$-brackets $\langle f\rangle_q$) 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 $\langle Q_k^{(p)}\rangle_q$ are quasimodular and find explicit expressions for them in terms of the $\langle Q_k\rangle_q$.

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Last update made Wed Feb 17 13:45:51 PST 2016.
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