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pro vyhledávání: '"Aymone, Marco"'
Autor:
Aymone, Marco
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 $V(x)$ is at least $\gg (\log x)(\log\log x)^{-1/2-\epsilon}$. Our new metho
Externí odkaz:
http://arxiv.org/abs/2409.19845
Autor:
Aymone, Marco
Inspired in 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 Rademacher random multiplicative function, $\sum_{n\leq x}f(n)n^{-\sigma
Externí odkaz:
http://arxiv.org/abs/2408.15589
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), 2017, pp. 1622-1657. These functions are periodic and $1$-pretentious
Externí odkaz:
http://arxiv.org/abs/2305.06260
Autor:
Aymone, Marco
We study two models of random multiplicative functions: Rademacher random multiplicative functions supported on the squarefree integers $f$, and Rademacher random completely multiplicative functions $f^*$. We prove that the partial sums $\sum_{n\leq
Externí odkaz:
http://arxiv.org/abs/2303.14682
Let $F(\sigma)=\sum_{n=1}^\infty \frac{X_n}{n^\sigma}$ be a random Dirichlet series where $(X_n)_{n\in\mathbb{N}}$ are independent standard Gaussian random variables. We compute in a quantitative form the expected number of zeros of $F(\sigma)$ in th
Externí odkaz:
http://arxiv.org/abs/2302.00616
Autor:
Aymone, Marco
We consider the problem of $\Omega$ bounds for the partial sums of a modified character, \textit{i.e.}, a completely multiplicative function $f$ such that $f(p)=\chi(p)$ for all but a finite number of primes $p$, where $\chi$ is a primitive Dirichlet
Externí odkaz:
http://arxiv.org/abs/2210.06153
Autor:
Aymone, Marco
We present a class of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ with bounded partial sums. The novelty here is that our functions do not need to have modulus bounded by $1$. The key feature is that they pretend to be the constant function
Externí odkaz:
http://arxiv.org/abs/2110.03401
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.
Comment: 10 pages, added comments from the referee and two figur
Comment: 10 pages, added comments from the referee and two figur
Externí odkaz:
http://arxiv.org/abs/2103.05413
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 $o(x^{1/k})$. Further, if we assume the Generalized Riemann Hypothesis, then w
Externí odkaz:
http://arxiv.org/abs/2101.00279
Autor:
Aymone, Marco
Let $1/2\leq\beta<1$, $p$ be a generic prime number and $f_\beta$ be a random multiplicative function supported on the squarefree integers such that $(f_\beta(p))_{p}$ is an i.i.d. sequence of random variables with distribution $\mathbb{P}(f(p)=-1)=\
Externí odkaz:
http://arxiv.org/abs/2009.09240