P. Zenz

collaborators

3 papers

math.NT2025

Second Moment of Central Values of Half-Integral Weight Modular Forms and Subconvexity

Steven Creech, Henry Twiss, Zhining Wei +1

We let $f$ be a half-integral weight modular form of weight $κ > 4$ on $Γ_{0} (4)$ that is an eigenfunction of all Hecke operators $T_{n}$ , so that $T_{n} f = Λ_{f} (n) n^{\frac{κ - 1}{2}} f$ . Let…

math.NT2021

Quantum variance for holomorphic Hecke cusp forms on the vertical geodesic

Peter Zenz

We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth, compactly supported test functions. The variance is related to an averaged shifted-co…

math.NT2021

Sharp bound for the fourth moment of holomorphic Hecke cusp forms

Peter Zenz

We prove that the fourth moment of holomorphic Hecke cusp forms is bounded provided that the Riemann Hypothesis holds for an appropriate degree 8 L-function. We accomplish this usi…