Jacques Benatar

activity

20132024

most citedMoments of polynomials with random multiplicative coefficients

14 citations · 18 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2024

A short-interval Hildebrand-Tenenbaum theorem

Jacques Benatar

In the late eighties, Hildebrand and Tenenbaum proved an asymptotic formula for the number of positive integers below $x$ , having exactly $ν$ distinct prime divisors: $π_ν(x) \sim…

math.NT2022

Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

Jacques Benatar, Alon Nishry

For $X (n)$ a Steinhaus random multiplicative function, we study the maximal size of the random Dirichlet polynomial $D_{N} (t) = \frac{1}{N} n \leq N \sum X (n) n^{i t},$ wit…

math.CV2021★ 1 cited

Zero distribution of power series and binary correlation of coefficients

Jacques Benatar, Alexander Borichev, Mikhail Sodin

We study the distribution of zeroes of power series with infinite radius of convergence. The coefficients of the series have the form $ξ (n) a (n)$ , where $a$ is a smooth sequence of…

math.NT2020★ 14 cited

Moments of polynomials with random multiplicative coefficients

Jacques Benatar, Alon Nishry, Brad Rodgers

For $X (n)$ a Rademacher or Steinhaus random multiplicative function, we consider the random polynomials $P_{N} (θ) = \frac{1}{N} n \leq N \sum X (n) e (n θ),$ and show that the…

math.PR2019★ 1 cited

The "pits effect" for entire functions of exponential type and the Wiener spectrum

Jacques Benatar, Alexander Borichev, Mikhail Sodin

Given a sequence $ξ : Z_{+} \to C$ , we find a simple spectral condition which guarantees the angular equidistribution of the zeroes of the Taylor series \[ F_ξ(z)…

math-ph2017

Planck-scale distribution of nodal length of arithmetic random waves

Jacques Benatar, Domenico Marinucci, Igor Wigman

We study the nodal length of random toral Laplace eigenfunctions ("arithmetic random waves") restricted to decreasing domains ("shrinking balls"), all the way down to Planck scale.…

math.NT2017

Random waves on $T^{3}$ : nodal area variance and lattice point correlations

Jacques Benatar, Riccardo W. Maffucci

We consider the ensemble of random Gaussian Laplace eigenfunctions on $T^{3} = R^{3} / Z^{3}$ (` $3 d$ arithmetic random waves'), and study the distribution of their…

math.NT2015★ 2 cited

Goldbach versus de Polignac numbers

Jacques Benatar

In this note we use recent developments in sieve theory to highlight the interplay between Goldbach and de Polignac numbers. Assuming that the primes have level of distribution gre…

math.NT2013

The existence of small prime gaps in subsets of the integers

Jacques Benatar

We consider the problem of finding small prime gaps in various sets of integers $C$ . Following the work of Goldston-Pintz-Yildirim, we will consider collections of natura…

A short-interval Hildebrand-Tenenbaum theorem

Extremal bounds for Dirichlet polynomials with random multiplicative coefficients

Zero distribution of power series and binary correlation of coefficients

Moments of polynomials with random multiplicative coefficients

The "pits effect" for entire functions of exponential type and the Wiener spectrum

Planck-scale distribution of nodal length of arithmetic random waves

Random waves on T3: nodal area variance and lattice point correlations

Goldbach versus de Polignac numbers

The existence of small prime gaps in subsets of the integers

Random waves on $T^{3}$ : nodal area variance and lattice point correlations