Soft bounds for local triple products and the subconvexity-QUE implication for GL₂

2025/05/19 by Nelson, Paul D.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.13256

Abstract

We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.

Citations

• Effective correlation and decorrelation for newforms, and weak subconvexity for L-functions
• Dissipation of correlations of holomorphic cusp forms
• The Weyl bound for triple product L-functions
• Hida families and p-adic triple product L-functions
• Quantum variance on quaternion algebras, III
• Triple product formula and mass equidistribution on modular curves of level N
• The Quantum Variance of the Modular Surface
• Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels
• Triple Product L Functions and Quantum Chaos on SL(2,C)
• On the Ramanujan conjecture over number fields
• Quantum unique ergodicity for SL₂(Z)\H
• Rankin Triple Products and Quantum Chaos
• Mass equidistribution for Hecke eigenforms
• Sparse equidistribution problems, period bounds, and subconvexity
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)

Related

• The subconvexity bound for triple product L-function in level aspect
• Rankin Triple Products and Quantum Chaos
• Triple Product L Functions and Quantum Chaos on SL(2,C)
• Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels
• Eisenstein Quasimodes and QUE