G. Molteni

activity

20182025

collaborators

Showing math.NTShow all

7 papers · 1 filter

math.NT2025

A lower bound for the number of Egyptian fractions

Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1

An Egyptian fraction is a sum of the form $1/ n_{1} + \dots + 1/ n_{r}$ where $n_{1}, \dots, n_{k}$ are distinct positive integers. We prove explicit lower bounds for the cardinality of the…

math.NT2024

The first and second moment for the length of the period of the continued fraction expansion for $d$

Francesco Battistoni, Loïc Grenié, Giuseppe Molteni

Let $d$ be any positive and non square integer. We prove an upper bound for the first two moments of the length $T (d)$ of the period of the continued fraction expansion for $\sqrt{…

math.NT2021

An elementary proof for a generalization of a Pohst's inequality

Francesco Battistoni, Giuseppe Molteni

Let $P_{n} (y_{1}, \dots, y_{n}) := \prod_{1 \leq i < j \leq n} (1 - \frac{y _{i}}{y _{j}})$ and $P_{n} := sup_{(y_{1}, \dots, y_{n})} P_{n} (y_{1}, \dots, y_{n})$ where the supremum is taken over the $n…

math.NT2019

Counting Egyptian fractions

Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1

For any integer $N \geq 1$ , let $E_{N}$ be the set of all Egyptian fractions employing denominators less than or equal to $N$ . We give upper and lower bounds for the cardi…

math.NT2019

Conditional upper bound for the k-th prime ideal with given Artin symbol

Loïc Grenié, Giuseppe Molteni

We prove an explicit upper bound for the k-th prime ideal with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.

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…