Parabolic eigenvarieties via overconvergent cohomology

D Barrera Salazar, C Williams - Mathematische Zeitschrift, 2021 - Springer
Let GG be a connected reductive group over QQ such that G= G/Q _p G= G/Q p is quasi-split,
and let Q ⊂ GQ⊂ G be a parabolic subgroup. We introduce parahoric overconvergent …

‐adic ‐functions of Bianchi modular forms

C Williams - Proceedings of the London Mathematical Society, 2017 - Wiley Online Library
The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn
Stevens, gives a beautiful and effective construction of the p‐adic L‐function of a modular …

-adic -functions of Hilbert cusp forms and the trivial zero conjecture

D Barrera, M Dimitrov, A Jorza - Journal of the European Mathematical …, 2021 - ems.press
We prove a strong form of the trivial zero conjecture at the central point for the p-adic L-
function of a non-critically refined self-dual cohomological cuspidal automorphic …

On -adic -functions for in finite slope Shalika families

DB Salazar, M Dimitrov, C Williams - arXiv preprint arXiv:2103.10907, 2021 - arxiv.org
In this paper, we prove new results on the geometry of the cuspidal eigenvariety for
$\mathrm {GL} _ {2n} $ over a totally real number field $ F $ at classical points admitting …

Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

D Barrera Salazar, C Williams - Selecta Mathematica, 2021 - Springer
Let K be an imaginary quadratic field. In this article, we study the eigenvariety for GL 2/K,
proving an étaleness result for the weight map at non-critical classical points and a …

Overconvergent cohomology of Hilbert modular varieties and -adic -functions

D Barrera Salazar - Annales de l'Institut Fourier, 2018 - numdam.org
The construction and study of p-adic analytic L-functions for elliptic modular forms has been
extensively studied by several authors using different approaches. In [14] the authors …

On -adic -functions for Hilbert modular forms

J Bergdall, D Hansen - arXiv preprint arXiv:1710.05324, 2017 - arxiv.org
We construct $ p $-adic $ L $-functions associated with $ p $-refined cohomological
cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our …

Exceptional zeros and ℒ-invariants of Bianchi modular forms

D Barrera Salazar, C Williams - Transactions of the American Mathematical …, 2019 - ams.org
Let $ f $ be a Bianchi modular form, that is, an automorphic form for $\mathrm {GL} _2 $ over
an imaginary quadratic field $ F $. In this paper, we prove an exceptional zero conjecture in …

On the GL(2n) eigenvariety: branching laws, Shalika families and -adic -functions

DB Salazar, M Dimitrov, A Graham, A Jorza… - arXiv preprint arXiv …, 2022 - arxiv.org
In this paper, we prove that a GL (2n)-eigenvariety is etale over the (pure) weight space at
non-critical Shalika points, and construct multi-variabled $ p $-adic $ L $-functions varying …

Algebracity and the -adic Interpolation of Special -values for certain Classical Groups

Y Jin - arXiv preprint arXiv:2305.19113, 2023 - arxiv.org
In this paper, we calculate the ramified local integrals in the doubling method and present an
integral representation of standard $ L $-functions for classical groups. We explicitly …