Chris Williams

activity

20242026

collaborators

8 papers

math.NT2026

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

Chris Williams

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

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.NT2026

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.NT2025

P-adic L-functions for GL(3)

David Loeffler, Chris Williams

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

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.NT2025

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 $I ¨ $ is a cuspidal automorphic representation of $GL_{2 n} (A)$ , then $I ¨ $ is a functorial transfer from $GSpin_{2 n + 1}$ i…

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

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

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

P-adic L-functions for GL(3)

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

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

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

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

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