Constructing Class invariants

TL;DR

This paper introduces a novel method leveraging Shimura reciprocity to both verify and discover new class invariants from modular functions of level N, advancing the computational tools in algebraic number theory.

Contribution

The paper presents a new approach based on Shimura reciprocity for constructing class invariants, expanding the capabilities beyond verification to include their explicit construction.

Findings

Successfully verified known class invariants using the new method

Demonstrated the ability to find previously unknown class invariants

Enhanced understanding of the relationship between modular functions and class invariants

Abstract

Shimura reciprocity law allows us to verify that a modular function is a class invariant. Here we present a new method based on Shimura reciprocity that allows us not only to verify but to find new class invariants from a modular function of level $N$.