Densities for Elliptic Curves over Global Function Fields

2023/01/26 by Yao, Andrew
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2301.11437

Abstract

Let K be a global function field. We obtain a set of formulas for the densities of the Kodaira types and Tamagawa numbers of elliptic curves over a completion of K that is independent of the field's characteristic. Furthermore, for a finite field F and real numbers s and ε such that s>1 and ε>0, we prove that there exists a global function field K such that the full constant field of K is F and the value of the zeta function of K at s is less than 1+ε.

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