Quaternionic and algebraic modular forms: structure and applications

Abstract: Modular forms on definite quaternion algebras are amenable to exact calculation by algebraic methods, and are related to classical modular forms via the Jacquet-Langlands correspondence. I will describe some structural results on quaternionic modular forms and applications to computing modular forms, Eisenstein congruences and central $L$-values. Along the way, I will discuss issues and progress toward analogues for algebraic modular forms on higher rank groups.

number theoryrepresentation theory

Audience: researchers in the topic

MIT number theory seminar

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