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A $p$-adic approach to the existence of level-raising congruences

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abstract

We construct level-raising congruences between $p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the $n^\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer $n = 1, 3, \dots, 25$.

fields

cs.LG 1

years

2024 1

verdicts

REJECT 1

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