Akashi series of Selmer groups

Abstract

We 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 [arXiv:math/0404431], 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.

13 pages

References in corpus (4)

• The GL_2 main conjecture for elliptic curves without complex multiplication
• Generalised Euler characteristics of Selmer groups
• Selmer Groups over p-adic Lie Extensions I
• On the leading terms of Zeta isomorphisms and p-adic L-functions in non-commutative Iwasawa theory

Cited by in corpus (4)

• A remark on the ${\mathfrak{M}}_H(G)$-conjecture and Akashi series
• Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p
• Non-commutative Iwasawa theory of abelian varieties over global function fields
• On order of vanishing of characteristic elements