References of "Perucca, Antonella 50028796"
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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 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 detailThe order of the reductions of an algebraic integer
Perucca, Antonella UL

in Journal of Number Theory (2015)

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See detailExplicit Kummer Theory for the rational numbers
Perucca, Antonella UL; Sgobba, Pietro UL; Tronto, Sebastiano 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.)

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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. Let a \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]{a}):K(\zeta_m)], where n divides m, is ... [more ▼]

Let K be a number field. Let a \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]{a}):K(\zeta_m)], where n divides m, is known to be bounded independently of n and m. For some families of number fields we describe an explicit algorithm that provides formulas for all the above Kummer degrees (the formulas involve a finite case distinction). Our algorithm can be implemented in Sagemath. [less ▲]

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

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

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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 detailReductions of points on algebraic groups II
Bruin, Peter; Perucca, Antonella UL

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See detailMultisets in arithmetics
Perucca, Antonella UL

(n.d.)

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See detailKummer theory for number fields and the reductions of algebraic numbers II
Perucca, Antonella UL; Sgobba, Pietro 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*. 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 uniformity 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 detailThe problem of detecting linear dependence
Perucca, Antonella UL

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

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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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