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Anil Venkatesh : The Arithmetic of Modular Forms

In this talk, we investigate modular forms and their many connections to number theory. Modular forms are analytic functions on the upper half complex plane that satisfy certain functional equations. They arise in many contexts in number theory: from partitions of integers, to arithmetical divisor functions, to cutting edge research on special values of the Riemann zeta function. We discuss both classical and modern examples, with a view toward illustrating the profound connections between analysis, topology, and number theory.

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