Marco Aymone

activity

20142026

most citedLaw of the iterated logarithm for a random Dirichlet series

10 citations · 48 across the 19 of their papers we have counts for

collaborators

22 papers

math.NT2026

Quantitative linear independence for square roots

Marco Aymone, Samuel Figueredo, Siddharth Iyer +1

We consider the problem of finding lower bounds for integer linear combinations of $a_{1}, \dots, a_{K}$ , where $a_{1}, \dots, a_{K}$ are positive integers such that their squa…

math.NT2025

$Ω$ -bounds for the partial sums of some modified Dirichlet characters II

Marco Aymone, Ana Paula Chaves, Maria Eduarda Ramos

A modified Dirichlet character $f$ is a completely multiplicative function such that for some Dirichlet character $χ$ , $f (p) = χ (p)$ for all but a finite number of primes $p \in S$ , a…

math.NT2024

Sign changes of the partial sums of a random multiplicative function III: Average

Marco Aymone

Let $V (x)$ be the number of sign changes of the partial sums up to $x$ , say $M_{f} (x)$ , of a Rademacher random multiplicative function $f$ . We prove that the averaged value of $V (x)$ …

math.NT2024

On the positivity of some weighted partial sums of a random multiplicative function

Marco Aymone

Inspired by the papers by Angelo and Xu, Q.J Math., 74, pp. 767-777, and improvements by Kerr and Klurman, arXiv:2211.05540, we study the probability that the weighted sums of a Ra…

math.NT2024

On the expected number of roots of a random Dirichlet polynomial

Marco Aymone, Caio Bueno

Let $T > 0$ and consider the random Dirichlet polynomial $S_{T} (t) = R e \sum_{n \leq T} X_{n} n^{- 1/2 - i t}$ , where $(X_{n})_{n}$ are i.i.d. Gaussian random variables with mean $0$ and varian…

math.NT2023★ 1 cited

Convolution of periodic multiplicative functions and the divisor problem

Marco Aymone, Gopal Maiti, Olivier Ramaré +1

We study a certain class of arithmetic functions that appeared in Klurman's classification of $\pm 1$ multiplicative functions with bounded partial sums, c.f., Comp. Math. 153 (8),…

math.NT2023

Sign changes of the partial sums of a random multiplicative function II

Marco Aymone

We study two models of random multiplicative functions: Rademacher random multiplicative functions supported on the squarefree integers $f$ , and Rademacher random completely multip…

math.NT2023

How many real zeros does a random Dirichlet series have?

Marco Aymone, Susana Frómeta, Ricardo Misturini

Let $F (σ) = \sum_{n = 1}^{\infty} \frac{X _{n}}{n ^{σ}}$ be a random Dirichlet series where $(X_{n})_{n \in N}$ are independent standard Gaussian random variables. We compute in a quantit…

math.NT2022

$Ω$ -bounds for the partial sums of some modified Dirichlet characters

Marco Aymone

We consider the problem of $Ω$ bounds for the partial sums of a modified character, \textit{i.e.}, a completely multiplicative function $f$ such that $f (p) = χ (p)$ for all but a fini…

math.NT2021

Complex valued multiplicative functions with bounded partial sums

Marco Aymone

We present a class of multiplicative functions $f : N \to C$ with bounded partial sums. The novelty here is that our functions do not need to have modulus bounded by…

math.NT2021

Sign changes of the partial sums of a random multiplicative function

Marco Aymone, Winston Heap, Jing Zhao

We provide a simple proof that the partial sums $\sum_{n \leq x} f (n)$ of a Rademacher random multiplicative function $f$ change sign infinitely often as $x \to \infty$ , almost surely.

math.NT2021

Multiplicative functions supported on the $k$ -free integers with small partial sums

Marco Aymone, Caio Bueno, Kevin Medeiros

We provide examples of multiplicative functions $f$ supported on the $k$ -free integers such that at primes $f (p) = \pm 1$ and such that the partial sums of $f$ up to $x$ are $o(x^{1/…

math.NT2020

Random multiplicative functions: The Selberg-Delange class

Marco Aymone

Let $1/2 \leq β < 1$ , $p$ be a generic prime number and $f_{β}$ be a random multiplicative function supported on the squarefree integers such that $(f_{β} (p))_{p}$ is an i.i.d. sequence of…

math.PR2020

Bernoulli Hyperplane Percolation

Marco Aymone, Marcelo R. Hilário, Bernardo N. B. de Lima +1

We study a dependent site percolation model on the $n$ -dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We exte…

math.NT2020★ 9 cited

Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function

Marco Aymone, Winston Heap, Jing Zhao

We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high…

math.NT2020

On multiplicative functions which are small on average and zero free regions for the Riemann zeta function

Marco Aymone

In this short note we prove the following result: If a completely multiplicative function $f : N \to [- 1, 1]$ is small on average in the sense that $\sum_{n\leq x}f(n)\ll x^{1-…

math.PR2020★ 10 cited

Law of the iterated logarithm for a random Dirichlet series

Marco Aymone, Susana Frómeta, Ricardo Misturini

Let $(X_{n})_{n \in N}$ be a sequence of i.i.d. random variables with distribution $P (X_{1} = 1) = P (X_{1} = - 1) = 1/2$ . Let $F (σ) = \sum_{n = 1}^{\infty} X_{n} n^{- σ}$ . We prove…

math.NT2020

A note on prime number races and zero free regions for $L$ functions

Marco Aymone

Let $χ$ be a real and non-principal Dirichlet character, $L (s, χ)$ its Dirichlet $L$ -function and let $p$ be a generic prime number. We prove the following result: If for some $0\le…

math.NT2019★ 9 cited

A note on multiplicative functions resembling the Möbius function

Marco Aymone

We provide examples of multiplicative functions $f$ supported on the squarefree integers, such that on primes $f (p) = \pm 1$ and such that $M_{f} (x) := \sum_{n \leq x} f (n) = o (x)$ . F…

math.NT2019★ 1 cited

The Erdős discrepancy problem over the squarefree and cubefree integers

Marco Aymone

Let $g : N \to {- 1, 1}$ be a completely multiplicative function, $μ$ be the Möbius function and $μ_{2}^{2} (n)$ be the indicator that $n$ is cubefree. We prove that $f = μ^{2} g$ and $…

math.PR2019★ 10 cited

Real zeros of random Dirichlet series

Marco Aymone

Let $F (σ)$ be the random Dirichlet series $F (σ) = \sum_{p \in P} \frac{X _{p}}{p ^{σ}}$ , where $P$ is an increasing sequence of positive real numbers and $(X_p)_{p\in\mat…

math.NT2014★ 8 cited

Partial sums of biased random multiplicative functions

Marco Aymone, Vladas Sidoravicius

Let $P$ be the set of the primes. We consider a class of random multiplicative functions $f$ supported on the squarefree integers, such that ${f (p)}_{p \in P}$ …

Quantitative linear independence for square roots

Ω-bounds for the partial sums of some modified Dirichlet characters II

Sign changes of the partial sums of a random multiplicative function III: Average

On the positivity of some weighted partial sums of a random multiplicative function

On the expected number of roots of a random Dirichlet polynomial

Convolution of periodic multiplicative functions and the divisor problem

Sign changes of the partial sums of a random multiplicative function II

How many real zeros does a random Dirichlet series have?

Ω-bounds for the partial sums of some modified Dirichlet characters

Complex valued multiplicative functions with bounded partial sums

Sign changes of the partial sums of a random multiplicative function

Multiplicative functions supported on the k-free integers with small partial sums

Random multiplicative functions: The Selberg-Delange class

Bernoulli Hyperplane Percolation

Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function

On multiplicative functions which are small on average and zero free regions for the Riemann zeta function

Law of the iterated logarithm for a random Dirichlet series

A note on prime number races and zero free regions for L functions

A note on multiplicative functions resembling the Möbius function

The Erdős discrepancy problem over the squarefree and cubefree integers

Real zeros of random Dirichlet series

Partial sums of biased random multiplicative functions

$Ω$ -bounds for the partial sums of some modified Dirichlet characters II

$Ω$ -bounds for the partial sums of some modified Dirichlet characters

Multiplicative functions supported on the $k$ -free integers with small partial sums

A note on prime number races and zero free regions for $L$ functions