14 citations · 68 across the 17 of their papers we have counts for
19 papers
The variance of the number of lattice points in narrow sectors
Stephen Lester, Ezra Waxman, Nadav Yesha
We study the variance of the number of lattice points in smoothed narrow sectors, where the average is taken over the position of the sectors. There are three regimes corresponding…
On the supremum of random cusp forms
Bingrong Huang, Stephen Lester, Igor Wigman +1
A random ensemble of cusp forms for the full modular group is introduced. For a weight- cusp form, restricted to a compact subdomain of the modular surface, the true order of ma…
Almost sure asymptotics for the number variance of dilations of integer sequences
Christoph Aistleitner, Nadav Yesha
Let be a sequence of integers. We study the number variance of dilations modulo 1 in intervals of length , and establish pseudorandom…
On the number variance of sequences with small additive energy
Zonglin Li, Nadav Yesha
For a real-valued sequence , denote by the number of its first fractional parts lying in a random interval of size , where a…
On the number of lattice points in thin sectors
Ezra Waxman, Nadav Yesha
On the circle of radius centred at the origin, consider a ``thin'' sector about the fixed line with edges given by the lines , where $ε= ε_R \rightarro…
Intermediate-scale statistics for real-valued lacunary sequences
Nadav Yesha
We study intermediate-scale statistics for the fractional parts of the sequence , where is a positive, real-valued lacunary sequence,…
The distribution of spacings of real-valued lacunary sequences modulo one
Sneha Chaubey, Nadav Yesha
Let be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all , the pair correlation of $\…
Gap statistics and higher correlations for geometric progressions modulo one
Christoph Aistleitner, Simon Baker, Niclas Technau +1
Koksma's equidistribution theorem from 1935 states that for Lebesgue almost every , the fractional parts of the geometric progression are equidistributed mo…
Differences between Robin and Neumann eigenvalues
Zeev Rudnick, Igor Wigman, Nadav Yesha
Let be a bounded planar domain, with piecewise smooth boundary . For , we consider the Robin boundary value problem \[ -Δf =λf, \qquad \frac…
On the correlations of mod 1
Niclas Technau, Nadav Yesha
A well known result in the theory of uniform distribution modulo one (which goes back to Fejér and Csillag) states that the fractional parts of the sequence $(n^α)_{n\ge1…
The defect of toral Laplace eigenfunctions and Arithmetic Random Waves
Par Kurlberg, Igor Wigman, Nadav Yesha
We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenar…
Small scale equidistribution for a point scatterer on the torus
Nadav Yesha
We study the small scale distribution of the eigenfunctions of a point scatterer (the Laplacian perturbed by a delta potential) on two- and three-dimensional flat tori. In two dime…
CLT for Planck scale mass distribution of toral Laplace eigenfunctions
Igor Wigman, Nadav Yesha
We study the fine scale -mass distribution of toral Laplace eigenfunctions with respect to random position, in 2 and 3 dimensions. In 2d, under certain flatness assumptions on…
Pair correlation for quadratic polynomials mod 1
Jens Marklof, Nadav Yesha
It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. Most results towards an aff…
Uniform Distribution of Eigenstates on a Torus with Two Point Scatterers
Nadav Yesha
We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus. There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunction…
Nodal intersections for random waves on the 3-dimensional torus
Zeev Rudnick, Igor Wigman, Nadav Yesha
We investigate the number of nodal intersections of random Gaussian Laplace eigenfunctions on the standard three-dimensional flat torus with a fixed smooth reference curve, which h…
On the distribution of the divisor function and Hecke eigenvalues
Stephen Lester, Nadav Yesha
We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by É. Fouvry, S. Ganguly, E. Kow…
Quantum ergodicity for a point scatterer on the three-dimensional torus
Nadav Yesha
Consider a point scatterer (the Laplacian perturbed by a delta-potential) on the standard three-dimensional flat torus. Together with the eigenfunctions of the Laplacian which vani…
Eigenfunction statistics for a point scatterer on a three-dimensional torus
Nadav Yesha
In this paper we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this o…