# Number Theory Seminar

Presented by: Christophe Vignat

Title: “A Probabilistic Approach to Some Elliptic Functions”

Abstract:

Dan Romik recently published [1] some unexpected results about the Taylor coefficients of the Jacobi $\theta_3$ function. I will show how a probabilistic interpretation of Romik's results allows to interpret and extend them to the case of the $\theta_3(q)$ function with arbitrary parameter $q$.  I will also show how some elliptic functions such as Dedekind' eta function appear naturally in some probabilistic contexts.  This is joint work with Tanay Wakhare and Lin Jiu.

[1] D. Romik, The Taylor coefficients of the Jacobi theta constant $\theta_3$, The Ramanujan Journal, 2019.

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#### Location

#319 Colloquium Room Chase Building