Marco Aymone

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20192025

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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.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.NT2020

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

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

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…

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

Random multiplicative functions: The Selberg-Delange class

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

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

A note on multiplicative functions resembling the Möbius function

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

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