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arXiv · 2603.15446

$p$-adic $L$-functions for Hecke characters of totally imaginary fields

Guido Kings·Johannes Sprang
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Abstract

We construct $p$-adic $L$-functions interpolating critical $L$-values of algebraic Hecke characters for arbitrary unramified primes $p$ and any totally imaginary field. For non-ordinary primes, the only previously known case was that of imaginary quadratic extensions of $\mathbb{Q}$. One of the main ingredients is a new $p$-adic Fourier theory relating generic fibers of $p$-divisible groups to a general class of character varieties. Combining this with equivariant cohomology classes constructed in a previous paper allows us to construct the $p$-adic $L$-function.

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BibTeXRIS

Guido Kings, Johannes Sprang. 2026-03-16. $p$-adic $L$-functions for Hecke characters of totally imaginary fields. https://arxiv.org/abs/2603.15446

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