Pankaj Vishe: Dynamical methods for rapid computations of L-functions
Pankaj Vishe, KTH
Tid: To 2012-01-26 kl 15.15
Plats: Room 3721
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) up to 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}).