Congruence relations satisfied by quaternionic modular forms

TL;DR

This paper investigates specific congruence relations that quaternionic modular forms satisfy, contributing to the understanding of their algebraic and arithmetic properties within the broader context of modular forms of multiple variables.

Contribution

It introduces new congruence relations for quaternionic modular forms, enhancing the theoretical framework and potential applications in number theory.

Findings

Identified specific congruence relations for quaternionic modular forms

Enhanced understanding of algebraic structures of these forms

Potential implications for arithmetic properties of modular forms

Abstract

The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.