C. Sanna

activity

20122023

most citedOn the p-adic denseness of the quotient set of a polynomial image

12 citations · 106 across the 43 of their papers we have counts for

collaborators

Showing 2018Show all

7 papers · 1 filter

math.NT2018★ 2 cited

On numbers divisible by the product of their nonzero base $b$ digits

Carlo Sanna

For each integer $b \geq 3$ and every $x \geq 1$ , let $N_{b, 0} (x)$ be the set of positive integers $n \leq x$ which are divisible by the product of their nonzero base $b$ …

math.NT2018★ 6 cited

$p$ -adic denseness of members of partitions of $N$ and their ratio sets

Piotr Miska, Carlo Sanna

The ratio set of a set of positive integers $A$ is defined as $R (A) := {a / b : a, b \in A}$ . The study of the denseness of $R (A)$ in the set of positive real numbers is a classi…

math.NT2018★ 12 cited

On the p-adic denseness of the quotient set of a polynomial image

Piotr Miska, Nadir Murru, Carlo Sanna

The quotient set, or ratio set, of a set of integers $A$ is defined as $R (A) := {a / b : a, b \in A, b \neq = 0}$ . We consider the case in which $A$ is the image of $\mat…

math.NT2018

Small values of signed harmonic sums

Sandro Bettin, Giuseppe Molteni, Carlo Sanna

For every $τ \in R$ and every integer $N$ , let $m_{N} (τ)$ be the minimum of the distance of $τ$ from the sums $\sum_{n = 1}^{N} s_{n} / n$ , where $s_1, \ldots, s_n \in \{-1…

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★ 1 cited

Greedy approximations by signed harmonic sums and the Thue--Morse sequence

Sandro Bettin, Giuseppe Molteni, Carlo Sanna

Given a real number $τ$ , we study the approximation of $τ$ by signed harmonic sums $σ_{N} (τ) := \sum_{n \leq N} s_{n} (τ) / n$ , where the sequence of signs $(s_{N} (τ))_{N \in N}$ i…

math.NT2018

Waring's Theorem for Binary Powers

Daniel M. Kane, Carlo Sanna, Jeffrey Shallit

A natural number is a binary $k$ 'th power if its binary representation consists of $k$ consecutive identical blocks. We prove an analogue of Waring's theorem for sums of binary $k$ …

On numbers divisible by the product of their nonzero base b digits

p-adic denseness of members of partitions of N and their ratio sets