Daniele Mastrostefano

activity

20182021

n

with polynomial image coprime with the

n

th term of a linear recurrence

2 citations · 2 across the 6 of their papers we have counts for

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math.NT2021

An almost sure upper bound for random multiplicative functions on integers with a large prime factor

Daniele Mastrostefano

Let $f$ be a Rademacher or a Steinhaus random multiplicative function. Let $ε > 0$ small. We prove that, as $x \to + \infty$ , we almost surely have $$\bigg|\sum_{\sub…

math.NT2021

A lower bound for the variance in arithmetic progressions of some multiplicative functions close to $1$

Daniele Mastrostefano

We investigate lower bounds for the variance in arithmetic progressions of certain multiplicative functions "close" to $1$ . Specifically, we consider $α_{N}$ -fold divisor functions,…

math.NT2020

On maximal product sets of random sets

Daniele Mastrostefano

For every positive integer N and every $α \in [0, 1)$ , let $B (N, α)$ denote the probabilistic model in which a random set $A \subset {1, \dots, N}$ is constructed by choosing independ…

math.NT2020

A lower bound for the variance of generalized divisor functions in arithmetic progressions

Daniele Mastrostefano

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 ar…

math.NT2018

Positive proportion of short intervals containing a prescribed number of primes

Daniele Mastrostefano

We will prove that for every $m \geq 0$ there exists an $ε = ε (m) > 0$ such that if $0 < λ < ε$ and $x$ is sufficiently large in terms of $m$ and $λ$ , then $$|…

math.NT2018★ 2 cited

On numbers $n$ with polynomial image coprime with the $n$ th term of a linear recurrence

Daniele Mastrostefano, Carlo Sanna

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 $A_{F, G, h}$ be the se…

math.NT2018

An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences

Daniele Mastrostefano

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 $ℓ_{u} (m) = l c m (m, z_{u} (m))$ , for $(m, a_{2}) = 1$ , where $z_{u} (m)$ is t…

math.NT2018

Weighted Average Number of Prime $m$ -tuples lying on an Admissible $k$ -tuple of Linear Forms

Daniele Mastrostefano

We find an upper bound for the sum $\sum_{x < n \leq 2 x} 1_{P} (n + h_{i_{1}}) \dots 1_{P} (n + h_{i_{m + 1}}) w_{n}$ , where $(h_{i_{1}}, ..., h_{i_{m + 1}})$ is…

math.NT2018

Short intervals containing a prescribed number of primes

Daniele Mastrostefano

We prove that for every nonnegative integer $m$ there exists an $ε > 0$ such that if $λ \in (0, ε]$ and $x$ is sufficiently large in terms of $m$ , then the number o…

An almost sure upper bound for random multiplicative functions on integers with a large prime factor

A lower bound for the variance in arithmetic progressions of some multiplicative functions close to 1

On maximal product sets of random sets

A lower bound for the variance of generalized divisor functions in arithmetic progressions

Positive proportion of short intervals containing a prescribed number of primes

On numbers n with polynomial image coprime with the nth term of a linear recurrence

An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences

Weighted Average Number of Prime m-tuples lying on an Admissible k-tuple of Linear Forms

Short intervals containing a prescribed number of primes

A lower bound for the variance in arithmetic progressions of some multiplicative functions close to $1$

On numbers $n$ with polynomial image coprime with the $n$ th term of a linear recurrence

Weighted Average Number of Prime $m$ -tuples lying on an Admissible $k$ -tuple of Linear Forms