Paul D. Nelson

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20102022

most citedEquidistribution of cusp forms in the level aspect

28 citations · 140 across the 20 of their papers we have counts for

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Showing 2019 · math.NTShow all

4 papers · 2 filters

math.NT2019★ 6 cited

Bounds for twisted symmetric square $L$ -functions via half-integral weight periods

Paul D. Nelson

We establish the first moment bound $φ \sum L (φ \otimes φ \otimes Ψ, \frac{1}{2}) ≪_{ε} p^{5/4 + ε}$ for triple product $L$ -functions, where $Ψ$ is a fixed H…

math.NT2019★ 11 cited

Eisenstein series and the cubic moment for PGL(2)

Paul D. Nelson

Following a strategy suggested by Michel--Venkatesh, we study the cubic moment of automorphic $L$ -functions on $PGL_{2}$ using regularized diagonal periods of products…

math.NT2019★ 4 cited

Analytic newvectors for $GL_{n} (R)$

Subhajit Jana, Paul D. Nelson

We relate the analytic conductor of a generic irreducible representation of $GL_{n} (R)$ to the invariance properties of vectors in that representation. The relation…

math.NT2019

Quantum variance on quaternion algebras, III

Paul D. Nelson

We determine the asymptotic quantum variance of microlocal lifts of Hecke--Maass cusp forms on the arithmetic compact hyperbolic surfaces attached to maximal orders in quaternion a…

Bounds for twisted symmetric square L-functions via half-integral weight periods

Eisenstein series and the cubic moment for PGL(2)

Analytic newvectors for GLn​(R)

Quantum variance on quaternion algebras, III

Bounds for twisted symmetric square $L$ -functions via half-integral weight periods

Analytic newvectors for $GL_{n} (R)$