The Lambda-adic Shimura-Shintani-Waldspurger Correspondence

TL;DR

This paper extends the $\\Lambda$-adic Shintani lifting, a mathematical construction related to automorphic forms, from the classical setting of $GL_2(\mathbb{Q})$ to the more general context of indefinite quaternion algebras over $\mathbb{Q}$.

Contribution

It introduces a generalized $\\Lambda$-adic Shimura-Shintani-Waldspurger correspondence applicable to indefinite quaternion algebras, broadening the scope of existing lifting theories.

Findings

Established a new $\\Lambda$-adic correspondence for quaternion algebras.

Extended classical lifting techniques to a broader algebraic setting.

Provided foundational results for future research in automorphic forms and number theory.

Abstract

We generalize the $\Lambda$-adic Shintani lifting for $GL_2(Q)$ to indefinite quaternion algebras over $Q$.