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math.NT2024
Sign changes of the partial sums of a random multiplicative function III: Average
Marco Aymone
Let be the number of sign changes of the partial sums up to , say , of a Rademacher random multiplicative function . We prove that the averaged value of …
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 and consider the random Dirichlet polynomial , where are i.i.d. Gaussian random variables with mean and varian…