References of "Perucca, Antonella 50028796"
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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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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 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 detailThe 15 puzzle
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 detailMultisets in arithmetics
Perucca, Antonella UL

in Multimengen in der Arithmetik (2019)

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See detailTrigonometry for the multiples of 3 degrees
Perucca, Antonella UL; Stranen, Deborah UL

Article for general public (2019)

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See detailMultisets
Perucca, Antonella UL

Article for general public (2019)

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See detailThe Art Gallery Problem
Perucca, Antonella UL

Article for general public (2019)

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See detailReductions of points on algebraic groups
Lombardo, Davide; Perucca, Antonella UL

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

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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)

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

in International Journal of Number Theory (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 detailThe problem of detecting linear dependence
Perucca, Antonella UL

in Rivista di Matematica della Universita di Parma (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 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)

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See detailDriehoeken met onderling 5 gelijke zijden en hoeken
Perucca, Antonella UL; Van den Broek, Luc

Article for general public (2018)

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