Dynamical methods for rapid computations of L-functions

by Prof. Pankaj Vishe (Max-Planck Institute, Bonn, Germany)

Friday 6 May 2011, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

Let f be a holomorphic or Maass cusp form on the upper half plane. We use the slow divergence of the horocycle flow on the upper half plane to get an algorithm to compute $L(f, 1/2 +iT)$ upto a maximum error $O(T^{-\gamma)$ using $o(T^{7/8+\eta})$ operations. Here $\gamma $ and $\eta $ are any positive numbers and the constants in O are independent of T. We thus improve the current approximate functional equation based algorithms which have complexity $O(T^{1+\eta})$.