Jerusalem Mathematics Colloquium

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Thursday, 27th December 2001, 4:00 pm
Mathematics Building, Lecture Hall 2

Irwin Kra
(SUNY, Stony Brook)

Uniformizations and theta-constant identities

(Based on joint work with Hershel M. Farkas)

Abstract: One variable theta functions are useful tools in complex analysis, number theory and combinatorics. They provide examples of uniformizations of Riemann surfaces that can serve as models for a more general theory.

After motivating an approach to the study of one variable theta-functions through problems arising from Kleinian groups and Ahlfors' finiteness theorem, we will take a leisurely tour of an elliptic paradise and its number theoretic and combinatorial regions, including a discussion of multiplicative functions related to the Ramanujan tau-function. The emphasis will be on function theoretic derivations of theta-constant identities and their use to uniformize (compact) Riemann surfaces. If time permits we will discuss products of theta-constants that result in constant functions, identities not connected to Riemann surface theory, and infinite product expansions of theta-constant derivatives (generalizing the Jacobi derivative formula).

Coffee, Cookies at the faculty lounge at 3:30.

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