References of "Perucca, Antonella 50028796"
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See detailDer 50cm lange Gliedermaßstab
Foyen, Andy UL; Perucca, Antonella UL

Scientific Conference (2022)

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See detailGeometrie der römischen Mosaiken
Perucca, Antonella UL

Scientific Conference (2022)

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See detailExplicit Kummer generators for cyclotomic extensions
Hoermann, Fritz; Perucca, Antonella UL; Sgobba, Pietro UL et al

in JP Journal of Algebra, Number Theory and Applications (2022)

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See detailMinorities in Mathematics
Perucca, Antonella UL

Article for general public (2022)

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See detailSharing calculations to understand arithmetical algorithms and parallel computing
Andrusiak, Rich; Perucca, Antonella UL

in Mathematics Teacher (2022)

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See detailArithmetic Billiards
Perucca, Antonella UL; Reguengo da Sousa, Joe; Tronto, Sebastiano UL

in Recreational Mathematics Magazine (2022)

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See detailProportionalitätsrechner für Menschen mit einer Dyskalkulie
Perucca, Antonella UL; Ronk, Pit Ferdy UL

Scientific Conference (2022)

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See detailEvery number is the beginning of a power of 2
Perucca, Antonella UL

Article for general public (2021)

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See detailStaircase numbers
Perucca, Antonella UL

Article for general public (2021)

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See detailThe degree of Kummer extensions of number fields
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano UL

in International Journal of Number Theory (2021)

Let K be a number field, and let \alpha_1, ... , \alpha_r be elements of K* which generate a subgroup of K* of rank r. Consider the cyclotomic-Kummer extensions of K given by K(\zeta_n, \sqrt[n_1]{\alpha ... [more ▼]

Let K be a number field, and let \alpha_1, ... , \alpha_r be elements of K* which generate a subgroup of K* of rank r. Consider the cyclotomic-Kummer extensions of K given by K(\zeta_n, \sqrt[n_1]{\alpha_1}, ... , \sqrt[n_r]{\alpha_r}), where n_i divides n for all i. There is an integer x such that these extensions have maximal degree over K(\zeta_g, \sqrt[g_1]{\alpha_1}, ... , \sqrt[g_r]{\alpha_r}), where g=\gcd(n,x) and g_i=\gcd(n_i,x). We prove that the constant x is computable. This result reduces to finitely many cases the computation of the degrees of the extensions K(\zeta_n, \sqrt[n_1]{\alpha_1}, ... , \sqrt[n_r]{\alpha_r}) over K. [less ▲]

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

in Manuscripta Mathematica (2021)

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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 ▲]

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See detailThe 15 puzzle
Perucca, Antonella UL

Article for general public (2020)

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See detailFour points, two distances
Perucca, Antonella UL

Article for general public (2020)

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See detailThe seven bridges of Königsberg
Perucca, Antonella UL

Article for general public (2020)

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See detailThe degree of non-Galois Kummer extensions of number fields
Perucca, Antonella UL

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

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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 ▲]

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

Article for general public (2020)

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