Chris Williams

activity

20142026

most cited

P

-adic

L

-functions of Bianchi modular forms

18 citations · 92 across the 17 of their papers we have counts for

collaborators

19 papers

math.NT2026

The non-abelian Leopoldt conjecture and equalities of $L$ -invariants

Daniel Barrera Salazar, Andrew Graham, Chris Williams

Let $G$ be a reductive group quasi-split at $p$ . Using arguments of Hansen--Thorne, we show that under the non-abelian Leopoldt conjecture (NALC), Hansen's $p$ -adic overconvergent…

math.NT2025

Local-global compatibility and the exceptional zero conjecture for GL(3)

Daniel Barrera Salazar, Andrew Graham, Chris Williams

We prove exceptional zero conjectures for $p$ -ordinary regular algebraic cuspidal automorphic representations of $GL_{3} (A)$ which are Steinberg at $p$ . We make no…

math.NT2023★ 1 cited

An introduction to $p$ -adic $L$ -functions

Joaquín Rodrigues Jacinto, Chris Williams

These expository notes introduce $p$ -adic $L$ -functions and the foundations of Iwasawa theory. We focus on Kubota--Leopoldt's $p$ -adic analogue of the Riemann zeta function, which…

math.NT2023★ 3 cited

On $p$ -refined Friedberg-Jacquet integrals and the classical symplectic locus in the $GL_{2 n}$ eigenvariety

Daniel Barrera Salazar, Andrew Graham, Chris Williams

Friedberg--Jacquet proved that if $π$ is a cuspidal automorphic representation of $GL_{2 n} (A)$ , then $π$ is a functorial transfer from $GSpin_{2 n + 1}$ if…

math.NT2023

On $p$ -adic $L$ -functions for symplectic representations of GL(N) over number fields

Chris Williams

Let $F$ be a number field, and $π$ a regular algebraic cuspidal automorphic representation of $GL_{N} (A_{F})$ of symplectic type. When $π$ is spherical at all primes…

math.NT2022★ 2 cited

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

Daniel Barrera Salazar, Mladen Dimitrov, Andrew Graham +2

In this paper, we prove that a $GL (2 n)$ -eigenvariety is étale over the (pure) weight space at non-critical Shalika points, and construct multi-variable $p$ -adic $L$ -functi…

math.NT2021

P-adic L-functions for GL(3)

David Loeffler, Chris Williams

Let $Π$ be a regular algebraic cuspidal automorphic representation (RACAR) of $GL_{3} (A_{Q})$ . When $Π$ is $p$ -nearly-ordinary for the maximal standard par…

math.NT2021

Overconvergent cohomology, $p$ -adic $L$ -functions and families for $GL (2)$ over CM fields

Daniel Barrera Salazar, Chris Williams

The use of overconvergent cohomology in constructing $p$ -adic $L$ -functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been estab…

math.NT2021

On $p$ -adic $L$ -functions for $G L_{2 n}$ in finite slope Shalika families

Daniel Barrera Salazar, Mladen Dimitrov, Chris Williams

In this paper, we propose and explore a new connection in the study of $p$ -adic $L$ -functions and eigenvarieties. We use it to prove results on the geometry of the cuspidal eigenva…

math.NT2020★ 6 cited

Arithmetic of p-irregular modular forms: families and p-adic L-functions

Adel Betina, Chris Williams

Let $f_{new}$ be a classical newform of weight $\geq 2$ and prime to $p$ level. We study the arithmetic of $f_{new}$ and its unique $p$ -stabilisation $f$ when $f_…

math.NT2020★ 9 cited

Parabolic eigenvarieties via overconvergent cohomology

Daniel Barrera Salazar, Chris Williams

Let $G^{'}$ be a connected reductive group over $Q$ such that $G = G^{'} / Q_{p}$ is quasi-split, and let $Q \subset G$ be a parabolic subgroup. We introduce parahoric over…

math.NT2019★ 2 cited

Stark-Heegner cycles attached to Bianchi modular forms

Guhan Venkat, Chris Williams

Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F, and let P be a prime of F at which f is new. Let K be a quadratic exten…

math.NT2019★ 2 cited

Overconvergent Hilbert modular forms via perfectoid modular varieties

Christopher Birkbeck, Ben Heuer, Chris Williams

We give a new construction of $p$ -adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The de…

math.NT2018★ 16 cited

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

Daniel Barrera Salazar, Chris Williams, Carl Wang-Erickson

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…

math.NT2018★ 6 cited

P-adic Asai L-functions of Bianchi modular forms

David Loeffler, Chris Williams

The Asai (or twisted tensor) $L$ -function of a Bianchi modular form $Ψ$ is the $L$ -function attached to the tensor induction to $Q$ of its associated Galois representation…

math.NT2017★ 14 cited

$L$ -invariants and exceptional zeros of Bianchi modular forms

Daniel Barrera Salazar, Chris Williams

Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F. In this paper, we prove an exceptional zero conjecture in the case wher…

math.NT2016★ 12 cited

P-adic L-functions for GL(2)

Daniel Barrera Salazar, Chris Williams

Since Rob Pollack and Glenn Stevens used overconvergent modular symbols to construct p-adic L-functions for non-critical slope rational modular forms, the theory has been extended…

math.NT2016★ 1 cited

Lifting non-ordinary cohomology classes for SL(3)

Chris Williams

In this paper, we present a generalisation of a theorem of David and Rob Pollack. In 'A construction of rigid analytic cohomology classes for congruence subgroups of SL(3,Z)', they…

math.NT2014★ 18 cited

$P$ -adic $L$ -functions of Bianchi modular forms

Chris Williams

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 for…

The non-abelian Leopoldt conjecture and equalities of L-invariants

Local-global compatibility and the exceptional zero conjecture for GL(3)

An introduction to p-adic L-functions

On p-refined Friedberg-Jacquet integrals and the classical symplectic locus in the GL2n​ eigenvariety

On p-adic L-functions for symplectic representations of GL(N) over number fields

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

P-adic L-functions for GL(3)

Overconvergent cohomology, p-adic L-functions and families for GL(2) over CM fields

On p-adic L-functions for GL2n​ in finite slope Shalika families

Arithmetic of p-irregular modular forms: families and p-adic L-functions

Parabolic eigenvarieties via overconvergent cohomology

Stark-Heegner cycles attached to Bianchi modular forms

Overconvergent Hilbert modular forms via perfectoid modular varieties

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

P-adic Asai L-functions of Bianchi modular forms

L-invariants and exceptional zeros of Bianchi modular forms

P-adic L-functions for GL(2)

Lifting non-ordinary cohomology classes for SL(3)

P-adic L-functions of Bianchi modular forms

The non-abelian Leopoldt conjecture and equalities of $L$ -invariants

An introduction to $p$ -adic $L$ -functions

On $p$ -refined Friedberg-Jacquet integrals and the classical symplectic locus in the $GL_{2 n}$ eigenvariety

On $p$ -adic $L$ -functions for symplectic representations of GL(N) over number fields

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

Overconvergent cohomology, $p$ -adic $L$ -functions and families for $GL (2)$ over CM fields

On $p$ -adic $L$ -functions for $G L_{2 n}$ in finite slope Shalika families

$L$ -invariants and exceptional zeros of Bianchi modular forms

$P$ -adic $L$ -functions of Bianchi modular forms