Algebraicity of L-values attached to Quaternionic Modular Forms

TL;DR

This paper proves the algebraicity of certain L-values linked to quaternionic modular forms, extending existing methods to non-tube type symmetric spaces and making key aspects explicit.

Contribution

It introduces the algebraicity proof for L-values in the non-tube type case, expanding the scope of the doubling method for quaternionic modular forms.

Findings

Established algebraicity of L-values for non-tube type symmetric spaces

Explicit descriptions of doubling embedding and coset decomposition

Defined algebraicity of modular forms via CM points

Abstract

In this paper we prove the algebraicity of some L-values attached to quaternionic modular forms. We follow the rather well established path of the doubling method. Our main contribution is that we include the case where the corresponding symmetric space is of non-tube type. We make various aspects very explicit such as, the doubling embedding, coset decomposition, and the definition of algebraicity of modular forms via CM points.