Pietro Sgobba

activity

20202026

most citedThe distribution of the multiplicative index of algebraic numbers over residue classes

1 citations · 1 across the 6 of their papers we have counts for

collaborators

7 papers

math.NT2026

Conflict-avoiding codes and near-primitive roots

C. G. Karthick Babu, Pieter Moree, Sunil Kumar Pasupulati +1

An important role in the theory of conflict-avoiding codes is played by a quantity involving the multiplicative order of $4$ modulo $d$ , with $d$ running over all positive divisors…

math.NT2025

Unconditional results for Artin-type problems over number fields

Pietro Sgobba

Let $K$ be a number field and let $G$ be a finitely generated subgroup of $K^{\times}$ . For all but finitely many primes $p$ of $K$ , the reduction $(G mod p)$ g…

math.NT2023★ 1 cited

The distribution of the multiplicative index of algebraic numbers over residue classes

Pieter Moree, Antonella Perucca, Pietro Sgobba

Let $K$ be a number field and $G$ a finitely generated torsion-free subgroup of $K^{\times}$ . Given a prime $p$ of $K$ we denote by $ind_{p} (G)$ the index o…

math.NT2022

Unified treatment of Artin-type problems II

Olli Järviniemi, Antonella Perucca, Pietro Sgobba

This work concerns Artin's Conjecture on primitive roots and related problems for number fields. Let $K$ be a number field and let $W_{1}$ to $W_{n}$ be finitely generated subgroups of…

math.NT2022

Prime divisors of $ℓ$ -Genocchi numbers and the ubiquity of Ramanujan-style congruences of level $ℓ$

Pieter Moree, Pietro Sgobba

Let $ℓ$ be any fixed prime number. We define the $ℓ$ -Genocchi numbers by $G_{n} := ℓ (1 - ℓ^{n}) B_{n}$ , with $B_{n}$ the $n$ -th Bernoulli number. They are integers. We introduce and…

math.NT2021

Divisibility conditions on the order of the reductions of algebraic numbers

Pietro Sgobba

Let $K$ be a number field, and let $G$ be a finitely generated subgroup of $K^{\times}$ . Without relying on the Generalized Riemann Hypothesis we prove an asymptotic formula for the…

math.NT2020

On the distribution of the order and index for the reductions of algebraic numbers

Pietro Sgobba

Let $α_{1}, \dots, α_{r}$ be algebraic numbers in a number field $K$ generating a subgroup of rank $r$ in $K^{\times}$ . We investigate under GRH the number of primes $p$ of $K$ …

Conflict-avoiding codes and near-primitive roots

Unconditional results for Artin-type problems over number fields

The distribution of the multiplicative index of algebraic numbers over residue classes

Unified treatment of Artin-type problems II

Prime divisors of ℓ-Genocchi numbers and the ubiquity of Ramanujan-style congruences of level ℓ

Divisibility conditions on the order of the reductions of algebraic numbers

On the distribution of the order and index for the reductions of algebraic numbers

Prime divisors of $ℓ$ -Genocchi numbers and the ubiquity of Ramanujan-style congruences of level $ℓ$