References of "Perucca, Antonella 50028796"
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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 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 detailThe PytEuk puzzle
Perucca, Antonella UL

Diverse speeches and writings (2018)

We present an original mathematical exhibit.

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

E-print/Working paper (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)

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See detailThe prime divisors of the number of points on abelian varieties
Perucca, Antonella UL

in Journal de Theorie des Nombres de Bordeaux (2015)

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

E-print/Working paper (n.d.)

Let $K$ be a number field, and let $G$ be a finitely generated and torsion-free subgroup of $K^\times$. We are interested in computing the degree of the cyclotomic-Kummer extension $K(\sqrt[n]{G})$ over ... [more ▼]

Let $K$ be a number field, and let $G$ be a finitely generated and torsion-free subgroup of $K^\times$. We are interested in computing the degree of the cyclotomic-Kummer extension $K(\sqrt[n]{G})$ over $K$, where $\sqrt[n]{G}$ consists of all $n$-th roots of the elements of $G$. We develop the theory of entanglements introduced by Lenstra, and apply it to compute the above degrees. [less ▲]

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See detailKummer theory for one-dimensional tori
Perucca, Antonella UL; Navas Orozco, Jesús

E-print/Working paper (n.d.)

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See detailExplicit Kummer theory for quadratic fields
Hörmann, Fritz; Perucca, Antonella UL; Sgobba, Pietro UL et al

E-print/Working paper (n.d.)

Let K be a number field, and let \alpha \in K be an algebraic number which is neither 0 nor a root of unity. The ratio between n and the Kummer degree [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)], where n ... [more ▼]

Let K be a number field, and let \alpha \in K be an algebraic number which is neither 0 nor a root of unity. The ratio between n and the Kummer degree [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)], where n divides m, is known to be bounded independently of n and m. For some families of quadratic number fields we describe an explicit algorithm that provides formulas for all those Kummer degrees. In particular, for the given fields we are able to give explicit expressions for the Kummer extensions contained in a cyclotomic extension. [less ▲]

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See detailKummer extensions of number fields (the case of rank 2)
Perucca, Antonella UL

E-print/Working paper (n.d.)

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

E-print/Working paper (n.d.)

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

E-print/Working paper (n.d.)

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See detailSOS Sudoku
Perucca, Antonella UL

E-print/Working paper (n.d.)

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

E-print/Working paper (n.d.)

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. Moreover, if n, n_1, ... , n_r are powers of some prime number, then we prove that one can compute parametric formulas (with parameters n, n_1, ... , n_r) for the degree of the above extensions. [less ▲]

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See detailThe Hardest Logic Puzzle Ever
Perucca, Antonella UL

E-print/Working paper (n.d.)

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