Research Interests

Most of my work in mathematics has been in number theory. My primary contribution has been a limit formula, proved jointly with Don Zagier, for the first derivative of the L-series of modular forms at the point s=1, in terms of the heights of points on the Jacobians of modular curves. These points are the classes of divisors supported on points of complex multiplication, and our formula constitutes a modern chapter in the history of that subject. One consequence is a method for showing that certain cubic equations have infinitely many rational solutions, when they have, on average, a large number of solutions modulo primes.

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Section 11: Mathematics