Marco Aymone

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math.NT2025

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.NT2025

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.NT2025

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.NT2025

$I^c ◯$ -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 $I ¨ $ , $f (p) = I ¨ (p)$ for all but a finite number of primes $p \in S$ ,…

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

On the expected number of roots of a random Dirichlet polynomial

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

I^c◯-bounds for the partial sums of some modified Dirichlet characters II

$I^c ◯$ -bounds for the partial sums of some modified Dirichlet characters II