Quadratic modular symbols on Shimura curves

TL;DR

This paper extends the concept of quadratic modular symbols and their connection to quadratic p-adic L-functions from modular curves to more general Shimura curves, providing a new framework for their study.

Contribution

It introduces a method to attach quadratic modular symbols and quadratic p-adic L-functions to general Shimura curves, broadening their applicability.

Findings

Established a link between quadratic modular symbols and p-adic L-functions on Shimura curves.

Extended previous concepts from modular curves to a wider class of Shimura curves.

Provided a new approach for studying p-adic L-functions in the context of Shimura varieties.

Abstract

We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic p-adic L-functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic p-adic L-functions to more general Shimura curves.