Rankin-Selberg L-functions in cyclotomic towers, II

Jeanine Van Order

Published 2012-07-06, updated 2014-10-18Version 2

We establish an analogue of Mazur's conjecture in the non self-dual setting, with applications to bounding ranks of elliptic curves in abelian extensions of imaginary quadratic fields. The methods used in this work are completely algebraic, using the theory of cyclic basechange with the existence of suitable $p$-adic $L$-functions to reduce the problem to known estimates in general self-dual setting over totally real number fields.