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On the Average of p-Selmer Rank in Quadratic Twist Families of Elliptic Curves over Function Field
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Version 1
: Received: 30 January 2021 / Approved: 1 February 2021 / Online: 1 February 2021 (09:54:56 CET)
How to cite: Wang, N.; Park, S. On the Average of p-Selmer Rank in Quadratic Twist Families of Elliptic Curves over Function Field. Preprints 2021, 2021020005 Wang, N.; Park, S. On the Average of p-Selmer Rank in Quadratic Twist Families of Elliptic Curves over Function Field. Preprints 2021, 2021020005
Abstract
We show that if the quadratic twist family of a given elliptic curve over F_q[t] with char(F_q) > 5 has an element whose Neron model has a multiplicative reduction away from infinity, then the average p-Selmer rank is p+1 in large q-limit for almost all primes p.
Keywords
Selmer group; quadratic twist; elliptic curve
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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