Peter Humphries

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20242026

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math.NT2026

Rankin--Selberg Subconvexity via Spectral Reciprocity

Peter Humphries, Liyang Yang

We establish explicit subconvex bounds for central values of Rankin--Selberg $L$ -functions $L (1/2, I ¨ \times I ¨ ^{'})$ associated with pairs of unitary cuspidal automorphic representation…

math.NT2025

New variants of arithmetic quantum ergodicity

Peter Humphries, Jesse Thorner

We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual $GL_{2}$ Hecke-Maass newforms over $Q$ as the level and Laplace eigenvalu…

math.NT2024

Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke-MaaÃ Cusp Forms on $SL_{2} (Z) \ SL_{2} (R)$

Ankit Bisain, Peter Humphries, Andrei Mandelshtam +2

It is a folklore result in arithmetic quantum chaos that quantum unique ergodicity on the modular surface with an effective rate of convergence follows from subconvex bounds for ce…

Rankin--Selberg Subconvexity via Spectral Reciprocity

New variants of arithmetic quantum ergodicity

Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke-MaaÃ Cusp Forms on SL2​(Z)\SL2​(R)

Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke-MaaÃ Cusp Forms on $SL_{2} (Z) \ SL_{2} (R)$