Research PaperNo Access

The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields

Igor E. Shparlinski

Department of Pure Mathematics, University of New South Wales, 2052 NSW, Australia

E-mail Address: igor.shparlinski@unsw.edu.au

https://doi.org/10.1142/S1793042119500246Cited by:0 (Source: Crossref)

Abstract

Over the last two decades, there has been a wave of activity establishing the Sato-Tate kind of distribution in various families of elliptic curves over prime fields. Typically the goal here is to prove this for families which are as thin as possible. We consider a function field analogue of this question, that is, for high degree extensions of a finite field where new effects allow us to study families, which are much thinner that those typically investigated over prime fields.

Keywords:

AMSC: 11G05, 11G20, 11T30

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