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Colloquium: Ken Ono (Univ of Virginia)

Wednesday, April 12
4:00 PM
203 TMCB

Title: Variants of Lehmer’s Conjecture

Abstract: Modular forms are generating functions of important quantities in arithmetic geometry, combinatorics, number theory, physics, and representation theory. Despite many deep developments in the arithmetic geometric and analytic aspects (e.g. Deligne’s proof of the Weil Conjectures, the development of Galois representations, Birch and Swinnerton-Dyer Conjecture, to name a few), some of the seminal questions about them remain open. Perhaps the most prominent of these is Lehmer’s Conjecture on the nonvanishing of modular form coefficients such as Ramanujan’s tau-function. In joint work with J. Balakrishnan, W. Craig, and W.-L. Tsai, the speaker has obtained the first results that establish that many integers are never modular form coefficients. This lecture is geared to a general audience