Peter Humphries

works on

automorphic forms 1 hecke-maaß cusp forms 1 heegner points 1 shifted convolution 1 spectral moments 1 sum of two squares 1

From the 1 of 4 linked papers with an AI index.

activity

20242026

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math.NT2026

Spectral fourth moments of Hecke--MaaÃ cusp forms

Edgar Assing, Peter Humphries

The paper proves near‑optimal bounds for the fourth spectral moment of Hecke–Maaß cusp forms evaluated at Heegner points and uses these bounds for shifted convolution sums involvin…

math.NT2025

Sparse Equidistribution of Geometric Invariants of Real Quadratic Fields

Peter Humphries, AsbjÃ¸rn Christian Nordentoft

Duke, Imamoglu, and TÃ³th have recently constructed a new geometric invariant, a hyperbolic orbifold, associated to each narrow ideal class of a real quadratic field. Furthermore,…

math.NT2025

$L^{p}$ -Norm Bounds for Automorphic Forms via Spectral Reciprocity

Peter Humphries, Rizwanur Khan

Let $g$ be a Hecke-Maass cusp form on the modular surface $SL_{2} (Z) \ H$ , namely an $L^{2}$ -normalised nonconstant Laplacian eigenfunction on ${\rm SL}_…

math.NT2024

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…

Spectral fourth moments of Hecke--MaaÃ cusp forms

Sparse Equidistribution of Geometric Invariants of Real Quadratic Fields

Lp-Norm Bounds for Automorphic Forms via Spectral Reciprocity

Archimedean Newform Theory for GLn​

Spectral fourth moments of Hecke--MaaÃ cusp forms

$L^{p}$ -Norm Bounds for Automorphic Forms via Spectral Reciprocity

Archimedean Newform Theory for $GL_{n}$