References of "Perucca, Antonella 50028796"
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See detailThe ABCD of cyclic quadrilaterals
Begalla, Engjell UL; Perucca, Antonella UL

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See detailKummer theory for number fields
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in Proceedings of the Roman Number Theory Association (2020)

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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 ▲]

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See detailDe zeven bruggen van Koningsbergen
Perucca, Antonella UL

Article for general public (2020)

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See detailDe 15-puzzel
Perucca, Antonella UL

Article for general public (2020)

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See detailVisualisierungen des Induktionsprinzips
Perucca, Antonella UL; Todorovic, Milko

in Beiträge zum Mathematikunterricht 2020 (2020)

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See detailVier punten, twee afstanden
Perucca, Antonella UL

in Uitwiskeling (2020)

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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 ▲]

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See detailVeelvouden van 3 graden
Perucca, Antonella UL; Stranen, Deborah UL

Article for general public (2019)

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See detailReductions of elliptic curves
Perucca, Antonella UL

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

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See detailHet kunstgalerijprobleem
Perucca, Antonella UL

Article for general public (2019)

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See detailAddendum to: Reductions of algebraic integers
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

E-print/Working paper (2019)

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 ▲]

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See detailKummer theory for number fields and the reductions of algebraic numbers
Perucca, Antonella UL; Sgobba, Pietro UL

E-print/Working paper (2019)

For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov-Ribet method) of the fact that if G is ... [more ▼]

For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov-Ribet method) of the fact that if G is a finitely generated and torsion-free multiplicative subgroup of a number field K having rank r, then the ratio between n^r and the Kummer degree [K(\zeta_n,\sqrt[n]{G}):K(\zeta_n)] is bounded independently of n. We then apply this result to generalise to higher rank a theorem of Ziegler from 2006 about the multiplicative order of the reductions of algebraic integers (the multiplicative order must be in a given arithmetic progression, and an additional Frobenius condition may be considered). [less ▲]

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See detailMultiverzameling
Perucca, Antonella UL

Article for general public (2019)

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See detailTactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind
Perucca, Antonella UL; Fiore, Tom; Lang, Alexander

in College Mathematics Journal (2018)

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See detailArithmetic billiards
Perucca, Antonella UL

Article for general public (2018)

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See detailMath around the Clock
Perucca, Antonella UL

Article for general public (2018)

This is an article for the general public about mathematical clocks. Several original mathematical clocks are also presented.

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See detailUnderstanding the Babylonian tablet ‘Plimpton 322’ with the decimal system
Perucca, Antonella UL; Stranen, Deborah

E-print/Working paper (2018)

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See detailReductions of algebraic integers II
Perucca, Antonella UL

in Association for Women in Mathematics Series (2018)

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See detailReductions of one-dimensional tori II
Perucca, Antonella UL

in Association for Women in Mathematics Series (2018)

Detailed reference viewed: 86 (1 UL)