Bianchi modular generalization of Stevens' non-vanishing conjecture

Let FF be the number field in the Bianchi modular setting, let pp) be a prime satisfying the residual non-vanishing hypotheses, and let Y\mathfrak{Y} be the set of finite order Hecke characters over FF whose conductor is πOF\pi\mathcal{O}_F for some prime element π\pi in the sets Pb,dP_{b,d} associated with pairs (b,d)S(Mp,N)(b,d)\in S(\mathfrak{M}_p,\mathfrak{N}). Let Lf(ϕ)\mathcal{L}_f(\phi) denote the normalized integral LL-value attached to the Bianchi Hecke eigenform ff. Generalized Stevens conjecture. Assume (Non-Eis)(\mathbf{Non\text{-}Eis}). Then there exist infinitely many Hecke characters ϕ\phi such that

Lf(ϕ) is a p-adic unit.\mathcal{L}_f(\phi)\text{ is a }p\text{-adic unit}.

This conjecture proposes the Bianchi modular analogue of Stevens' result; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Jaesung Kwon, “Bianchi modular symbols and p-adic L-functions”, arXiv:2108.05592 (2024).

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