An Effective Equidistribution Theorem
Prof. M. Ram Murty
Queen's University, Canada.
31-12-07

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Abstract

We will prove a new equidistribution theorem that has applications in a wide variety of contexts. This theorem is effective in that it also supplies error estimates. One important application is to the "vertical" distribution of the eigenvalues of the Hecke operator T_p, for a fixed prime p, which improves upon theorems of J.-P. Serre. In particular, we are able to discuss the factorization of the Jacobian of the modular curve X_0(N) into simple abelian varieties as N tends to infinity. More precisely, we can show the dimension of every simple abelian factor exceeds (log log N)^{1/2} for N sufficiently large.

Most of the talk and general discussion of equidistribution will be accessible to senior undergraduate students and beginning graduate students. This work is joint with Kaneenika Sinha.