P. Allen

activity

20122021

most citedDeformations of polarized automorphic Galois representations and adjoint Selmer groups

38 citations · 72 across the 10 of their papers we have counts for

collaborators

Showing 2021Show all

2 papers · 1 filter

math.NT2021

Congruences like Atkin's for the partition function

Scott Ahlgren, Patrick B. Allen, Shiang Tang

Let $p (n)$ be the ordinary partition function. In the 1960s Atkin found a number of examples of congruences of the form $p (Q^{3} ℓ n + β) \equiv 0 (mod ℓ)$ where $ℓ$ and $Q$ are…

math.NT2021★ 1 cited

Modularity of $PGL_{2} (F_{p})$ -representations over totally real fields

Patrick B. Allen, Chandrashekhar B. Khare, Jack A. Thorne

We study an analogue of Serre's modularity conjecture for projective representations $ρ : Gal (K / K) \to PGL_{2} (k)$ , where $…

Congruences like Atkin's for the partition function

Modularity of PGL2​(Fp​)-representations over totally real fields

Modularity of $PGL_{2} (F_{p})$ -representations over totally real fields