W. Verreault

activity

20212026

most citedNonlinear expansions in reproducing kernel Hilbert spaces

2 citations · 8 across the 19 of their papers we have counts for

collaborators

21 papers

math.NT2026

On the distribution of the minimal length of addition chains

Jean-Marie De Koninck, Nicolas Doyon, William Verreault

A sequence of integers $1 = a_{0} < a_{1} < \dots < a_{k} = n$ is called an addition chain of length $k$ if $a_{j} = a_{s} + a_{t}$ with $0 \leq s, t < j$ for all integers $j \in {1, 2, \dots, k}$ . We denote by…

math.PR2026

Fourier decay of Gaussian multiplicative chaos and boundary geometry

Marcu-Antone Orsoni, William Verreault

In this paper, we develop a new approach to studying the Fourier transform of Gaussian multiplicative chaos. We determine the Fourier dimension of these random measures on tori for…

math.NT2026

Almost sure upper bound for sums of random multiplicative functions and critical chaos

William Verreault

Let $f$ be a Steinhaus or Rademacher random multiplicative function. We use methods from the theory of critical chaos to improve on the best known upper bound for partial sums of r…

math.FA2026

A proof of conjectures of Esterle and Ransford on negative powers of contractions

William Verreault

Building on work of Ransford, we prove that whenever $E$ is a closed subset of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_{n} \to \infty$ such that i…

math.NT2025

Central limit theorems for random multiplicative functions over function fields

Declan Hoban, Jibran Iqbal Shah, Nadya-Catherine Ismail +2

We provide a sufficient characterization for subsets $A$ of the polynomial ring $F_{q} [t]$ for which partial sums of Steinhaus random multiplicative functions appr…

math.NT2025

On the minimal length of addition chains

Jean-Marie De Koninck, Nicolas Doyon, William Verreault

We denote by $ℓ (n)$ the minimal length of an addition chain leading to $n$ and we define the counting function $F (m, r) := # {n \in [2^{m}, 2^{m + 1}) : ℓ (n) \leq m + r},$ …

math.FA2024

The Cesàro operator on local Dirichlet spaces

Eugenio Dellepiane, Javad Mashreghi, Mostafa Nasri +1

The family of Cesàro operators $σ_{n}^{α}$ , $n \geq 0$ and $α \in [0, 1]$ , consists of finite rank operators on Banach spaces of analytic functions on the open unit disc. In this work, w…

math.NT2024

Moments of random multiplicative functions over function fields

Maximilian C. E. Hofmann, Annemily Hoganson, Siddarth Menon +2

Granville-Soundararajan, Harper-Nikeghbali-Radziwill, and Heap-Lindqvist independently established an asymptotic for the even natural moments of partial sums of random multiplicati…

math.FA2023★ 2 cited

Nonlinear expansions in reproducing kernel Hilbert spaces

Javad Mashreghi, William Verreault

We introduce an expansion scheme in reproducing kernel Hilbert spaces, which as a special case covers the celebrated Blaschke unwinding series expansion for analytic functions. The…

math.NT2023

On the tower factorization of integers

Jean-Marie De Koninck, William Verreault

Under the fundamental theorem of arithmetic, any integer $n > 1$ can be uniquely written as a product of prime powers $p^{a}$ ; factoring each exponent $a$ as a product of prime powers…

math.NT2023

Arithmetic functions at factorial arguments

Jean-Marie De Koninck, William Verreault

For various arithmetic functions $f : N \to R$ , the behavior of $f (n!)$ and that of $\sum_{n \leq N} f (n!)$ can be intriguing. For instance, for some functions $f$ , w…

math.RA2022

Classes of Holomorphic Multicomplex-Valued Functions Generated by Elliptic-Admissible Involutions

Nicolas Doyon, Pierre-Olivier Parisé, William Verreault

We classify and count the real-algebra involutions of the multicomplex algebra $MC (n)$ that map each element of its canonical monomial basis to a signed monomial…

math.CA2022

Failure of $L^{p}$ Symmetry of Zonal Spherical Harmonics

Gabriel Beiner, William Verreault

In this paper, we show that the 2-sphere does not exhibit symmetry of $L^{p}$ norms of eigenfunctions of the Laplacian for $p \geq 6$ . In other words, there exists a sequence of spher…

math.SP2022★ 1 cited

A counterexample to symmetry of $L^{p}$ norms of eigenfunctions

Gabriel Beiner, Nancy Mae Eagles, William Verreault +1

We answer a question of Jakobson and Nadirashvili on the asymptotic behavior of the $L^{p}$ norms of positive and negative parts of eigenfunctions of the Laplacian. More precisely, w…

math.MG2022

Plank theorems and their applications: a survey

William Verreault

Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank pro…

math.NT2021★ 2 cited

A conjectural asymptotic formula for multiplicative chaos in number theory

Daksh Aggarwal, Unique Subedi, William Verreault +2

We investigate a special sequence of random variables $A (N)$ defined by an exponential power series with independent standard complex Gaussians $(X (k))_{k \geq 1}$ . Introduced by H…

math.NT2021★ 1 cited

Sums of random multiplicative functions over function fields with few irreducible factors

Daksh Aggarwal, Unique Subedi, William Verreault +2

We establish a normal approximation for the limiting distribution of partial sums of random Rademacher multiplicative functions over function fields, provided the number of irreduc…

math.PR2021

On the probability of forming polygons from a broken stick

William Verreault

Break a stick at random at $n - 1$ points to obtain $n$ pieces. We give an explicit formula for the probability that every choice of $k$ segments from this broken stick can form a $k…

math.NT2021

Bounds for the counting function of the Jordan-Pólya numbers

Jean-Marie De Koninck, Nicolas Doyon, A. Arthur Bonkli Razafindrasoanaivolala +1

A positive integer $n$ is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pó…

math.NT2021★ 2 cited

Repetitions of multinomial coefficients and a generalization of Singmaster's conjecture

Jean-Marie de Koninck, Nicolas Doyon, William Verreault

Given two integers $k \geq 2$ and $a > 1$ , let $N_{k} (a)$ stand for the number of multinomial coefficients, with $k$ terms, equal to $a$ . We study the behavior of $N_{k} (a)$ and show that…

math.CO2021

MacMahon Partition Analysis: A discrete approach to broken stick problems

William Verreault

We propose a discrete approach to solve problems on forming polygons from broken sticks, which is akin to counting polygons with sides of integer length subject to certain Diophant…

On the distribution of the minimal length of addition chains

Fourier decay of Gaussian multiplicative chaos and boundary geometry

Almost sure upper bound for sums of random multiplicative functions and critical chaos

A proof of conjectures of Esterle and Ransford on negative powers of contractions

Central limit theorems for random multiplicative functions over function fields

On the minimal length of addition chains

The Cesàro operator on local Dirichlet spaces

Moments of random multiplicative functions over function fields

Nonlinear expansions in reproducing kernel Hilbert spaces

On the tower factorization of integers

Arithmetic functions at factorial arguments

Classes of Holomorphic Multicomplex-Valued Functions Generated by Elliptic-Admissible Involutions

Failure of Lp Symmetry of Zonal Spherical Harmonics

A counterexample to symmetry of Lp norms of eigenfunctions

Plank theorems and their applications: a survey

A conjectural asymptotic formula for multiplicative chaos in number theory

Sums of random multiplicative functions over function fields with few irreducible factors

On the probability of forming polygons from a broken stick

Bounds for the counting function of the Jordan-Pólya numbers

Repetitions of multinomial coefficients and a generalization of Singmaster's conjecture

MacMahon Partition Analysis: A discrete approach to broken stick problems

Failure of $L^{p}$ Symmetry of Zonal Spherical Harmonics

A counterexample to symmetry of $L^{p}$ norms of eigenfunctions