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

E-print/Working paper (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 detailHet kunstgalerijprobleem
Perucca, Antonella 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 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 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 detailDriehoeken met onderling 5 gelijke zijden en hoeken
Perucca, Antonella UL

Article for general public (2018)

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See detailThe PytEuk puzzle
Perucca, Antonella UL

Diverse speeches and writings (2018)

We present an original mathematical exhibit.

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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 detailReductions of one-dimensional tori II
Perucca, Antonella UL

in Association for Women in Mathematics Series (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 detailArithmetic billiards
Perucca, Antonella UL

Article for general public (2018)

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

E-print/Working paper (2017)

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See detailMultiplicative order and Frobenius symbol for the reductions of number fields
Perucca, Antonella UL

E-print/Working paper (2017)

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See detailThe 1-eigenspace for matrices in GL2(ℤℓ)
Lombardo, Davide; Perucca, Antonella UL

in New York Journal of Mathematics (2017)

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See detailThe Chinese Remainder Clock
Perucca, Antonella UL

in College Mathematics Journal (2017)

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See detailReductions of one-dimensional tori
Perucca, Antonella UL

in International Journal of Number Theory (2017)

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See detailReductions of algebraic integers
Debry, Christophe; Perucca, Antonella UL

in Journal of Number Theory (2016)

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See detailThe order of the reductions of an algebraic integer
Perucca, Antonella UL

in Journal of Number Theory (2015)

Detailed reference viewed: 63 (1 UL)