Akashi series of Selmer groups

Abstract

AbstractWe study the Selmer group of an elliptic curve over an admissible p-adic Lie extension of a number field F. We give a formula for the Akashi series attached to this module, in terms of the corresponding objects for the cyclotomic ℤp-extension and certain correction terms. This extends our earlier work [16], in particular since it applies to elliptic curves having split multiplicative reduction at some primes above p, in which case the Akashi series can have additional zeros.