Pietro Sgobba

collaborators

3 papers

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.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 $K$ …

Unified treatment of Artin-type problems II

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

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 $ℓ$