Effective Brauer-Siegel on some curves in $Y(1)^n$

TL;DR

This paper develops an effective version of Siegel's lower bounds for class numbers of imaginary quadratic fields within specific curves in the modular variety $Y(1)^n$, using the G-functions method.

Contribution

It introduces an effective approach to Siegel's bounds for class numbers on certain modular curves, leveraging the G-functions method of Yves André.

Findings

Established effective lower bounds for class numbers

Applied G-functions method to modular curves

Extended classical bounds to higher-dimensional settings

Abstract

We establish an effective version of Siegel's lower bounds for class numbers of imaginary quadratic fields in certain cures in $Y(1)^n$. Our proof goes through the G-functions method of Yves Andr\'e.