Peter Humphries

activity

20112026

most citedStandard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory

32 citations · 177 across the 24 of their papers we have counts for

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Showing 2020Show all

4 papers · 1 filter

math.RT2020★ 1 cited

The Newform $K$ -Type and $p$ -adic Spherical Harmonics

Peter Humphries

Let $K := GL_{n} (O)$ denote the maximal compact subgroup of $GL_{n} (F)$ , where $F$ is a nonarchimedean local field with ring of integers $O$ . We s…

math.NT2020★ 3 cited

Archimedean Newform Theory for $GL_{n}$

Peter Humphries

We introduce a new invariant, the conductor exponent, of a generic irreducible Casselman-Wallach representation of $GL_{n}$ that quantifies the extent to which this represen…

math.NT2020★ 6 cited

Towards a $GL_{n}$ variant of the Hoheisel phenomenon

Peter Humphries, Jesse Thorner

Let $π$ be a unitary cuspidal automorphic representation of $GL_{n}$ over a number field, and let $π ~$ be contragredient to $π$ . We prove effective upper and lower boun…

math.NT2020★ 6 cited

Distributing Points on the Torus via Modular Inverses

Peter Humphries

We study various statistics regarding the distribution of the points \[\left\{\left(\frac{d}{q},\frac{\overline{d}}{q}\right) \in \mathbb{T}^2 : d \in (\mathbb{Z}/q\mathbb{Z})^{\ti…

The Newform K-Type and p-adic Spherical Harmonics

Archimedean Newform Theory for GLn​

Towards a GLn​ variant of the Hoheisel phenomenon

Distributing Points on the Torus via Modular Inverses

The Newform $K$ -Type and $p$ -adic Spherical Harmonics

Archimedean Newform Theory for $GL_{n}$

Towards a $GL_{n}$ variant of the Hoheisel phenomenon