Automorphism group of split Cartan modular curves

TL;DR

This paper determines the automorphism groups of split Cartan modular curves $X_{split}(p)$ for all prime numbers, providing a comprehensive understanding of their symmetries.

Contribution

It explicitly computes the automorphism groups of $X_{split}(p)$ for all primes, a significant advancement in understanding these modular curves.

Findings

Automorphism groups are fully determined for all primes p.

Results reveal the structure and size of these automorphism groups.

The work enhances understanding of symmetries in modular curves.

Abstract

We determine the automorphism group of the split Cartan modular curves $X_{\operatorname{split}}(p)$ for all primes $p$.