References of "Perucca, Antonella 50028796"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailExplicit Kummer theory for quadratic fields
Hörmann, Fritz; Perucca, Antonella UL; Sgobba, Pietro UL et al

in JP Journal of Algebra, Number Theory and Applications (2021)

Let K be a quadratic number field and let \alpha \in K*. We present an explicit finite procedure to compute at once all Kummer degrees [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)] for n,m \geq 1 with n|m ... [more ▼]

Let K be a quadratic number field and let \alpha \in K*. We present an explicit finite procedure to compute at once all Kummer degrees [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)] for n,m \geq 1 with n|m, where \zeta_m denotes a primitive m-th root of unity. We can also replace \alpha by any finitely generated subgroup of K*. [less ▲]

Detailed reference viewed: 287 (13 UL)
Full Text
See detailEvery number is the beginning of a power of 2
Perucca, Antonella UL

Article for general public (2021)

Detailed reference viewed: 76 (7 UL)
Full Text
See detailStaircase numbers
Perucca, Antonella UL

Article for general public (2021)

Detailed reference viewed: 78 (1 UL)
Full Text
Peer Reviewed
See detailKummer theory for number fields via entanglement groups
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in Manuscripta Mathematica (2021)

Detailed reference viewed: 163 (7 UL)
Full Text
Peer Reviewed
See detailThe degree of non-Galois Kummer extensions of number fields
Perucca, Antonella UL

in Rivista di Matematica della Universita di Parma (2020), 11

Detailed reference viewed: 95 (2 UL)
Full Text
See detailThe ABCD of cyclic quadrilaterals
Begalla, Engjell UL; Perucca, Antonella UL

Article for general public (2020)

Detailed reference viewed: 147 (1 UL)
Full Text
See detailThe 15 puzzle
Perucca, Antonella UL

Article for general public (2020)

Detailed reference viewed: 109 (8 UL)
Full Text
See detailThe seven bridges of Königsberg
Perucca, Antonella UL

Article for general public (2020)

Detailed reference viewed: 59 (5 UL)
Full Text
See detailFour points, two distances
Perucca, Antonella UL

Article for general public (2020)

Detailed reference viewed: 74 (1 UL)
Full Text
Peer Reviewed
See detailKummer theory for number fields and the reductions of algebraic numbers II
Perucca, Antonella UL; Sgobba, Pietro UL

in Uniform Distribution Theory (2020)

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. For almost all primes p of K, we consider the order of the cyclic group (G mod p), and ask whether this number ... [more ▼]

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. For almost all primes p of K, we consider the order of the cyclic group (G mod p), and ask whether this number lies in a given arithmetic progression. We prove that the density of primes for which the condition holds is, under some general assumptions, a computable rational number which is strictly positive. We have also discovered the following equidistribution property: if \ell^e is a prime power and a is a multiple of \ell (and a is a multiple of 4 if \ell=2), then the density of primes p of K such that the order of (G mod p) is congruent to a modulo \ell^e only depends on a through its \ell-adic valuation. [less ▲]

Detailed reference viewed: 179 (19 UL)
Full Text
Peer Reviewed
See detailReductions of points on algebraic groups II
Bruin, Peter; Perucca, Antonella UL

in Glasgow Mathematical Journal (2020)

Detailed reference viewed: 43 (3 UL)
Full Text
Peer Reviewed
See detailExplicit Kummer theory for the rational numbers
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in International Journal of Number Theory (2020)

Let G be a finitely generated multiplicative subgroup of Q* having rank r. The ratio between n^r and the Kummer degree [Q(\zeta_m,\sqrt[n]{G}) : Q(\zeta_m)], where n divides m, is bounded independently of ... [more ▼]

Let G be a finitely generated multiplicative subgroup of Q* having rank r. The ratio between n^r and the Kummer degree [Q(\zeta_m,\sqrt[n]{G}) : Q(\zeta_m)], where n divides m, is bounded independently of n and m. We prove that there exist integers m_0, n_0 such that the above ratio depends only on G, \gcd(m,m_0), and \gcd(n,n_0). Our results are very explicit and they yield an algorithm that provides formulas for all the above Kummer degrees (the formulas involve a finite case distinction). [less ▲]

Detailed reference viewed: 252 (31 UL)
Full Text
Peer Reviewed
See detailAddendum to: Reductions of algebraic integers
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in Journal of Number Theory (2020)

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. We consider Kummer extensions of G of the form K(\zeta_{2^m}, \sqrt[2^n]G)/K(\zeta_{2^m}), where n \leq m. In ... [more ▼]

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. We consider Kummer extensions of G of the form K(\zeta_{2^m}, \sqrt[2^n]G)/K(\zeta_{2^m}), where n \leq m. In the paper "Reductions of algebraic integers" (J. Number Theory, 2016) by Debry and Perucca, the degrees of those extensions have been evaluated in terms of divisibility parameters over K(\zeta_4). We prove how properties of G over K explicitly determine the divisibility parameters over K(\zeta_4). This result has a clear computational advantage, since no field extension is required. [less ▲]

Detailed reference viewed: 171 (25 UL)
Full Text
See detailKummer theory for number fields
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in Proceedings of the Roman Number Theory Association (2020)

Detailed reference viewed: 94 (10 UL)
Full Text
See detailVisualisierungen des Induktionsprinzips
Perucca, Antonella UL; Todorovic, Milko

in Beiträge zum Mathematikunterricht 2020 (2020)

Detailed reference viewed: 61 (8 UL)
Full Text
Peer Reviewed
See detailReductions of points on algebraic groups
Lombardo, Davide; Perucca, Antonella UL

in Journal of the Institute of Mathematics of Jussieu (2019)

Detailed reference viewed: 96 (6 UL)
Full Text
Peer Reviewed
See detailMultiplicative order and Frobenius symbol for the reductions of number fields
Perucca, Antonella UL

in Research Directions in Number Theory, Association for Women in Mathematics, Series 19 (2019) (2019)

Detailed reference viewed: 122 (6 UL)
Full Text
See detailReductions of elliptic curves
Perucca, Antonella UL

in Proceedings of the Roman Number Theory Association (2019), 4

Detailed reference viewed: 122 (9 UL)
Full Text
See detailTrigonometry for the multiples of 3 degrees
Perucca, Antonella UL; Stranen, Deborah UL

Article for general public (2019)

Detailed reference viewed: 70 (8 UL)