Root numbers and parity of local Iwasawa invariants

Suman Ahmed; Chandrakant Aribam; Sudhanshu Shekhar

doi:10.1016/j.jnt.2017.01.019

Root numbers and parity of local Iwasawa invariants

Number Theory 2019-05-31 v2

Authors: Suman Ahmed , Chandrakant Aribam , Sudhanshu Shekhar

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Abstract

Given two elliptic curves $E_1$ and $E_2$ defined over the field of rational numbers, $\mathbb{Q}$ , with good reduction at an odd prime $p$ and equivalent mod $p$ Galois representation, we compare the $p$ -Selmer rank, global and local root numbers of $E_1$ and $E_2$ over number fields.

Keywords

elliptic curves root numbers Iwasawa invariants Selmer rank Galois representation parity

Cite

@article{arxiv.1608.08078,
  title  = {Root numbers and parity of local Iwasawa invariants},
  author = {Suman Ahmed and Chandrakant Aribam and Sudhanshu Shekhar},
  journal= {arXiv preprint arXiv:1608.08078},
  year   = {2019}
}

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16 pages

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