Number Theory Seminar: Alia Hamieh

Abstract:

Associated to a newform F in S2(Γ0(N)) and an anticyclotomic finite-order Hecke character χ of an imaginary quadratic field K, one defines the twisted L-function L(F,χ,s). Prof. Vatsal obtained various results pertaining to the non-vanishing modulo a prime λ in the algebraic closure of Q of the special values of these L-functions in the anticyclotomic tower of conductor p∞ over K when the sign in the functional equation is +1. In this talk, we report on a work in progress to establish some generalizations of such results.