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Reductions of algebraic integers II Perucca, Antonella in Association for Women in Mathematics Series (2018) Detailed reference viewed: 101 (7 UL)Understanding the Babylonian tablet ‘Plimpton 322’ with the decimal system Perucca, Antonella ; E-print/Working paper (2018) Detailed reference viewed: 51 (1 UL)The PytEuk puzzle Perucca, Antonella Diverse speeches and writings (2018) We present an original mathematical exhibit. Detailed reference viewed: 49 (10 UL)Reductions of points on algebraic groups ; Perucca, Antonella E-print/Working paper (2017) Detailed reference viewed: 44 (6 UL)The Chinese Remainder Clock Perucca, Antonella in College Mathematics Journal (2017) Detailed reference viewed: 38 (0 UL)Reductions of one-dimensional tori Perucca, Antonella in International Journal of Number Theory (2017) Detailed reference viewed: 83 (7 UL)The 1-eigenspace for matrices in GL2(ℤℓ) ; Perucca, Antonella in New York Journal of Mathematics (2017) Detailed reference viewed: 881 (3 UL)Multiplicative order and Frobenius symbol for the reductions of number fields Perucca, Antonella E-print/Working paper (2017) Detailed reference viewed: 79 (5 UL)Reductions of algebraic integers ; Perucca, Antonella in Journal of Number Theory (2016) Detailed reference viewed: 90 (4 UL)The order of the reductions of an algebraic integer Perucca, Antonella in Journal of Number Theory (2015) Detailed reference viewed: 84 (2 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: 72 (2 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: 83 (3 UL)Kummer theory for one-dimensional tori Perucca, Antonella ; E-print/Working paper (n.d.) Detailed reference viewed: 38 (6 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, 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 ▲] Detailed reference viewed: 66 (6 UL)Kummer extensions of number fields (the case of rank 2) Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 55 (14 UL)The degree of non-abelian Kummer extensions of number fields Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 58 (0 UL)Arithmetic Billiards Perucca, Antonella ; ; Tronto, Sebastiano E-print/Working paper (n.d.) Detailed reference viewed: 33 (0 UL)The degree of Kummer extensions of number fields Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano 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 ▲] Detailed reference viewed: 75 (8 UL)The Hardest Logic Puzzle Ever Perucca, Antonella E-print/Working paper (n.d.) Detailed reference viewed: 44 (0 UL) |
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