Abstract

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Generalized Borcherds products and two number theoretic applications

Ken Ono

At the 1994 ICM in Zurich, Borcherds introduced the notion of an automorphic infinite product. In this lecture I will discuss joint work with Jan Bruinier which gives automorphic infinite products arising from harmonic Maass forms. We will discuss two number theoretic applications:

1) Partitions
2) Central derivatives of modular L-functions.

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