Symmetric power functoriality for Hilbert modular forms

Abstract: Symmetric power functoriality is one of the basic cases of Langlands' functoriality conjectures and is the route to the proof of the Sato-Tate conjecture (concerning the distribution of the modulo $p$ point counts of an elliptic curve over $\mathbb{Q}$, as the prime $p$ varies).

I will discuss the proof of the existence of the symmetric power liftings of Hilbert modular forms of regular weight. This is joint work with James Newton.

number theory

Audience: researchers in the topic

London number theory seminar

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