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The 1-eigenspace for matrices in GL2(ℤℓ) ; Perucca, Antonella in New York Journal of Mathematics (2017) Detailed reference viewed: 868 (3 UL)The Chinese Remainder Clock Perucca, Antonella in College Mathematics Journal (2017) Detailed reference viewed: 36 (0 UL)Reductions of one-dimensional tori Perucca, Antonella in International Journal of Number Theory (2017) Detailed reference viewed: 72 (5 UL)Reductions of algebraic integers ; Perucca, Antonella in Journal of Number Theory (2016) Detailed reference viewed: 80 (4 UL)The prime divisors of the number of points on abelian varieties Perucca, Antonella in Journal de Theorie des Nombres de Bordeaux (2015) Detailed reference viewed: 65 (1 UL)The order of the reductions of an algebraic integer Perucca, Antonella in Journal of Number Theory (2015) Detailed reference viewed: 76 (2 UL)Explicit Kummer Theory for the rational numbers Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano E-print/Working paper (n.d.) Detailed reference viewed: 131 (21 UL)The degree of Kummer extensions of number fields Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano E-print/Working paper (n.d.) Detailed reference viewed: 51 (1 UL)Explicit Kummer theory for quadratic fields ; Perucca, Antonella ; Sgobba, Pietro 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 ▲] Detailed reference viewed: 15 (3 UL)Kummer extensions of number fields (the case of rank 2) II Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 13 (1 UL)Kummer extensions of number fields (the case of rank 2) Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 12 (2 UL)Reductions of points on algebraic groups II ; Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 6 (0 UL)Kummer theory for number fields and the reductions of algebraic numbers II Perucca, Antonella ; Sgobba, Pietro 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 ▲] Detailed reference viewed: 91 (9 UL)The problem of detecting linear dependence Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 53 (1 UL)Kummer theory for number fields via entanglement groups Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano 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 ▲] Detailed reference viewed: 73 (2 UL) |
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