Speaker: Kannappan Sampath
Affiliation: University of Michigan, U.S.A.
Title: A conjectural $p$-adic Jacquet-Langlands correspondence for weight 1 modular forms
Date and Time: October 27, 2023, 16:00:00 Hours
Venue: A-369
Asbtract: The Jacquet-Langlands correspondence asserts that an automorphic representation of GL(2) transfers to an automorphic representation of a quaternion algebra over $\mathbf{Q}$ if and only if the local component is square-integrable at places that are ramified in the quaternion algebra. It is known that the local representation of GL$_2(\mathbf{R})$ associated to a cusp form of weight one is not square-integrable. Thus, weight 1 forms do not transfer to a quaternion algebra ramified at infinity. Nevertheless, fixing a prime $p$ split in the quaternion algebra that is ramified at $\infty$, we will discuss a $p$-adic formulation of the Jacquet-Langlands correspondence that includes cuspidal newforms of weight 1 that are supercuspidal at $p$.
Affiliation: University of Michigan, U.S.A.
Title: A conjectural $p$-adic Jacquet-Langlands correspondence for weight 1 modular forms
Date and Time: October 27, 2023, 16:00:00 Hours
Venue: A-369
Asbtract: The Jacquet-Langlands correspondence asserts that an automorphic representation of GL(2) transfers to an automorphic representation of a quaternion algebra over $\mathbf{Q}$ if and only if the local component is square-integrable at places that are ramified in the quaternion algebra. It is known that the local representation of GL$_2(\mathbf{R})$ associated to a cusp form of weight one is not square-integrable. Thus, weight 1 forms do not transfer to a quaternion algebra ramified at infinity. Nevertheless, fixing a prime $p$ split in the quaternion algebra that is ramified at $\infty$, we will discuss a $p$-adic formulation of the Jacquet-Langlands correspondence that includes cuspidal newforms of weight 1 that are supercuspidal at $p$.