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arXiv · 1005.0394

Akashi series of Selmer groups

Sarah Livia Zerbes
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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.

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Sarah Livia Zerbes. 2010-05-03. Akashi series of Selmer groups. https://doi.org/10.1017/s0305004111000211

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