ON THE RANK OF QUADRATIC TWISTS OF ELLIPTIC CURVES OVER FUNCTION FIELDS

Type: Article

Publication Date: 2006-06-01

Citations: 20

DOI: https://doi.org/10.1142/s1793042106000528

Abstract

We prove quantitative upper bounds for the number of quadratic twists of a given elliptic curve E/F q (C) over a function field over a finite field that have rank ≥ 2, and for their average rank. The main tools are constructions and results of Katz and uniform versions of the Chebotarev density theorem for varieties over finite fields. Moreover, we conditionally derive a bound in some cases where the degree of the conductor is unbounded.

Locations

  • International Journal of Number Theory - View
  • CiteSeer X (The Pennsylvania State University) - View - PDF
  • HAL (Le Centre pour la Communication Scientifique Directe) - View

Similar Works

Action Title Year Authors
+ On the rank of quadratic twists of elliptic curvers over function fields 2005 Emmanuel Kowalski
+ PDF Chat A conditional determination of the average rank of elliptic curves 2016 Daniel Fiorilli
+ PDF Chat On the ranks of elliptic curves in families of quadratic twists over number fields 2014 Jung-Jo Lee
+ Average rank in families of quadratic twists: a geometric point of view 2015 Pierre Le Boudec
+ One-level density of the family of twists of an elliptic curve over function fields 2020 Antoine Comeau-Lapointe
+ PDF Chat Rank 0 Quadratic Twists of a Family of Elliptic Curves 2003 Gang Yu
+ PDF Chat One-level density of the family of twists of an elliptic curve over function fields 2022 Antoine Comeau-Lapointe
+ The average analytic rank of elliptic curves 2003 D. R. Heath‐Brown
+ Average rank of quadratic twists with a rational point of almost minimal height 2020 Joachim L. Petit
+ Elliptic curves with bounded ranks in function field towers 2011 Lisa Berger
+ Elliptic curves with bounded ranks in function field towers 2011 Lisa Berger
+ PDF Chat Elliptic curves with bounded ranks in function field towers 2012 Lisa Berger
+ PDF Chat Elliptic curves with a lower bound on 2-Selmer ranks of quadratic twists 2012 Zev Klagsbrun
+ On $2$-Selmer groups and quadratic twists of elliptic curves 2020 Daniel Barrera Salazar
Ariel Pacetti
Gonzalo Tornaría
+ Selmer Ranks of Quadratic Twists of Elliptic Curves 2011 Zev Klagsbrun
+ PDF Chat Experimental Data for Goldfeld’s Conjecture over Function Fields 2012 Salman Baig
Chris Hall
+ The Birch--Swinnerton-Dyer exact formula for quadratic twists of elliptic curves 2021 Shuai Zhai
+ PDF Chat 3-Isogeny Selmer groups and ranks of Abelian varieties in quadratic twist families over a number field 2019 Manjul Bhargava
Zev Klagsbrun
Robert J. Lemke Oliver
Ari Shnidman
+ On the Average of p-Selmer Rank in Quadratic Twist Families of Elliptic Curves over Function Field 2021 Niudun Wang
SunWoo Park
+ Ranks of elliptic curves in families of quadratic twists 1999 Karl Rubin
Alice Silverberg