A refinement of Sato-Tate conjecture

TL;DR

This paper proposes a refined version of the Sato-Tate conjecture focusing on the distribution of angles for primes and explores its implications for elliptic curve L-functions and random matrix theory.

Contribution

It introduces a refined conjecture on prime angle distributions and discusses its impact on elliptic curve L-functions and connections to random matrix theory.

Findings

Proposes a refined Sato-Tate conjecture.

Analyzes implications for elliptic curve L-functions.

Explores connections to random matrix theory.

Abstract

We propose a refined version of the Sato-Tate conjecture about the spacing distribution of the angle determined for each prime number. We also discuss its implications on $L$-function associated with elliptic curves in the relation to random matrix theory.