On $p$-adic Measures for Quaternionic Modular Forms

TL;DR

This paper investigates the special values of L-functions associated with quaternionic modular forms, providing integral representations and constructing p-adic measures to interpolate these values, advancing understanding in p-adic number theory.

Contribution

It introduces a new integral representation for twisted L-functions and constructs p-adic measures for quaternionic modular forms, enhancing tools for p-adic L-value interpolation.

Findings

Derived an integral representation for twisted L-functions.

Constructed p-adic measures interpolating special L-values.

Advanced methods for studying quaternionic modular forms.

Abstract

The purpose of this paper is to study the special values of the standard $L$-functions for quaternionic modular forms using the doubling method. We obtain an integral representation for the $L$-function twisted by a character and construct the $p$-adic measure interpolating certain special $L$-values.