Let f be a newform of even weight k, level M and character ψ and let g be a newform of even weight l, level N and character η. We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet L-functions, in the context of twisted modular L-functions associated to f and g. Using this result, we find a lower bound in terms of Q for the number of primitive Dirichlet cha...

In this paper, we study finite element approximations of the viscosity solution of the fully nonlinear Monge-Ampère equation, det(Du) = f (> 0) using the well-known nonconforming Morley element. Our approach is based on the vanishing moment method, which was recently proposed as a constructive way to approximate fully nonlinear second order equations by the author and Feng in [15]. The vanishin...

In this paper, which follows closely the talk given at the conference, I will sketch an example of a non-trivial element of K2 of a certain threefold, whose existence is related to the vanishing of an incomplete L-function of a modular form at s = 1. To explain how this fits into a general picture, we begin with a simple account, for the non-specialist, of some of the conjectures (mostly due to...

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with γ5. For a twisted Ginsparg-Wilson operator the spectrum is located on two arcs in the complex plane. Modes due to non-trivial topological charge of the underlyin...