5 papers
Quantitative nodal domain count for Maass forms
Peter Zenz
We consider a real even Hecke-Maass cusp form on the modular surface, with Laplace eigenvalue . We prove that its restriction to any fixed compact segment of the v…
Sharp effective equidistribution of closed geodesics in compact hyperbolic surfaces
Junehyuk Jung, Insung Park, Peter Zenz
We prove a sharp effective equidistribution theorem for closed geodesics on a compact hyperbolic surface. This is achieved by carefully analyzing the Selberg trace formula twisted…
Second Moment of Central Values of Half-Integral Weight Modular Forms and Subconvexity
Steven Creech, Henry Twiss, Zhining Wei +1
We let be a half-integral weight modular form of weight on that is an eigenfunction of all Hecke operators , so that . Let…
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…
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…