Ken Ono

Affiliation: University of Wisconsin

Email: ono@math.wisc.edu

Title Of Talk: Heegner divisors, L-functions and Maass forms

URL: http://www.math.wisc.edu/~ono/reprints/109.pdf

Abstract: In the 1980s, Gross and Zagier proved a deep theorem which gave a formula for central derivatives of modular L-functions in terms of the Neron-Tate heights of Heegner points. Also in the early 1980s, Waldspurger proved that the generating function for the central values of quadratic twists is essentially a modular form. It is natural to ask whether these two problems (values and derivatives) can be investigated in a uniform way by combining and extending features of these results. In joint work with Bruinier, we obtain such a result. We show that the Fourier expansions of harmonic Maass forms can be used to study both central values and derivatives of quadratic twists of modular L-functions. The key idea involves the arithmetic of Maass-Heegner points which are associated to canonical quadratic forms.

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