Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Mastrostefano, Daniele"'
An almost sure upper bound for random multiplicative functions on integers with a large prime factor
Autor:
Mastrostefano, Daniele
Let $f$ be a Rademacher or a Steinhaus random multiplicative function. Let $\varepsilon>0$ small. We prove that, as $x\rightarrow +\infty$, we almost surely have $$\bigg|\sum_{\substack{n\leq x\\ P(n)>\sqrt{x}}}f(n)\bigg|\leq\sqrt{x}(\log\log x)^{1/4
Externí odkaz:
http://arxiv.org/abs/2105.09565
Autor:
Mastrostefano, Daniele
We investigate lower bounds for the variance in arithmetic progressions of certain multiplicative functions "close" to $1$. Specifically, we consider $\alpha_N$-fold divisor functions, when $\alpha_N$ is a sequence of positive real numbers approachin
Externí odkaz:
http://arxiv.org/abs/2102.10589
Autor:
Mastrostefano, Daniele
For every positive integer N and every $\alpha\in [0,1)$, let $B(N, \alpha)$ denote the probabilistic model in which a random set $A\subset \{1,\dots,N\}$ is constructed by choosing independently every element of $\{1,\dots,N\}$ with probability $\al
Externí odkaz:
http://arxiv.org/abs/2005.04663
Autor:
Mastrostefano, Daniele
We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a result fo
Externí odkaz:
http://arxiv.org/abs/2004.05602
Autor:
Mastrostefano, Daniele
We will prove that for every $m\geq 0$ there exists an $\varepsilon=\varepsilon(m)>0$ such that if $0<\lambda<\varepsilon$ and $x$ is sufficiently large in terms of $m$ and $\lambda$, then $$|\lbrace n\leq x: |[n,n+\lambda\log n]\cap \mathbb{P}|=m\rb
Externí odkaz:
http://arxiv.org/abs/1812.11784
Autor:
Mastrostefano, Daniele, Sanna, Carlo
Publikováno v:
Bulletin of the Australian Mathematical Society 99 (2019), 23-33
Let $F$ be an integral linear recurrence, $G$ be an integer-valued polynomial splitting over the rationals, and $h$ be a positive integer. Also, let $\mathcal{A}_{F,G,h}$ be the set of all natural numbers $n$ such that $\gcd(F(n), G(n)) = h$. We prov
Externí odkaz:
http://arxiv.org/abs/1805.05114
Autor:
Mastrostefano, Daniele
Let $(u_n)_{n \geq 0}$ be a non-degenerate Lucas sequence, given by the relation $u_n=a_1 u_{n-1}+a_2 u_{n-2}$. Let $\ell_u(m)=lcm(m, z_u(m))$, for $(m,a_2)=1$, where $z_u(m)$ is the rank of appearance of $m$ in $u_n$. We prove that $$\sum_{\substack
Externí odkaz:
http://arxiv.org/abs/1805.02225
Autor:
Mastrostefano, Daniele
We find an upper bound for the sum $\sum_{x
Externí odkaz:
http://arxiv.org/abs/1804.06290
Autor:
Mastrostefano, Daniele
We prove that for every nonnegative integer $m$ there exists an $\varepsilon>0$ such that if $\lambda\in (0,\varepsilon]$ and $x$ is sufficiently large in terms of $m$, then the number of positive integers $n\leq x$ for which the interval $[n,n+\lamb
Externí odkaz:
http://arxiv.org/abs/1802.10327
