Minimal equations and values of generalized lambda functions

TL;DR

This paper investigates the minimal equations and specific values of generalized lambda functions, which are important in understanding the structure of modular function fields related to principal congruence subgroups.

Contribution

It provides new insights into the minimal equations and value computations of generalized lambda functions, expanding the understanding of their algebraic properties.

Findings

Derived minimal equations for generalized lambda functions

Computed specific values of these functions

Enhanced understanding of their role in modular function fields

Abstract

In our preceding article, we defined a generalized lambda function and showed that the genaralized lambda function and the modular invariant function generate the modular function field with respect to a principal congruence subgroup. In this article we shall study a minimal equation and values of the genaralized lambda function.