On the rank of quadratic twists of elliptic curvers over function fields
Emmanuel Kowalski
Abstract
We prove quantitative upper bounds for the number of quadratic twists of a given elliptic curve E/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.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad