Tim Huber

Affiliation: University of Texas - Rio Grande Valley

Email: timothy.huber@utrgv.edu

Title Of Talk: Higher level Ramanujan-Sato series for $1/\pi$.

Abstract: A systematic construction for Ramanujan-Sato expansions from McKay-Thompson series is given. Expansions for each divisor of the order of the Monster are derived, and a uniform interpretation is given for series parameters as generators of invariant function fields for subgroups of $\Gamma_{0}(n)$. Relations between the generators extend reciprocal identities satisfied by eta quotients and the continued fractions of Rogers-Ramanujan and Göllnitz-Gordon. Complete lists of rational and quadratic series are derived from singular values of the parameters. Heuristics will be given to minimize the order of recurrences defining the series expansions. This is joint work with Daniel Schultz and Dongxi Ye.

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