A geometric introduction to transcendence questions on values of modular forms

TL;DR

This paper surveys key developments in transcendental number theory, focusing on Nesterenko's theorem on Eisenstein series and exploring the geometric aspects of transcendence questions related to modular forms.

Contribution

It provides a geometric perspective on transcendence results for values of modular forms, highlighting recent advances and open problems.

Findings

Nesterenko's theorem on Eisenstein series

Geometric interpretation of transcendence results

Open problems on periods and modular forms

Abstract

We survey some key developments in the theory of transcendental numbers, paying special attention to Nesterenko's theorem on values of Eisenstein series and emphasizing its underlying geometric aspects. We finish with a brief discussion on periods and related open problems.