![]() Foyen, Andy ![]() ![]() Scientific Conference (2022) Detailed reference viewed: 17 (3 UL)![]() Perucca, Antonella ![]() Scientific Conference (2022) Detailed reference viewed: 26 (0 UL)![]() ; Perucca, Antonella ![]() ![]() in JP Journal of Algebra, Number Theory and Applications (2022) Detailed reference viewed: 120 (16 UL)![]() Perucca, Antonella ![]() Article for general public (2022) Detailed reference viewed: 63 (7 UL)![]() ; Perucca, Antonella ![]() in Mathematics Teacher (2022) Detailed reference viewed: 122 (10 UL)![]() Perucca, Antonella ![]() ![]() in Recreational Mathematics Magazine (2022) Detailed reference viewed: 97 (9 UL)![]() Perucca, Antonella ![]() ![]() Scientific Conference (2022) Detailed reference viewed: 37 (5 UL)![]() Perucca, Antonella ![]() Article for general public (2021) Detailed reference viewed: 64 (5 UL)![]() Perucca, Antonella ![]() Article for general public (2021) Detailed reference viewed: 65 (0 UL)![]() Perucca, Antonella ![]() ![]() ![]() in International Journal of Number Theory (2021) 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. This result reduces to finitely many cases the computation of the degrees of the extensions K(\zeta_n, \sqrt[n_1]{\alpha_1}, ... , \sqrt[n_r]{\alpha_r}) over K. [less ▲] Detailed reference viewed: 200 (12 UL)![]() Perucca, Antonella ![]() ![]() Speeches/Talks (2021) Detailed reference viewed: 49 (11 UL)![]() Perucca, Antonella ![]() ![]() ![]() in Manuscripta Mathematica (2021) Detailed reference viewed: 148 (6 UL)![]() ; Perucca, Antonella ![]() ![]() in JP Journal of Algebra, Number Theory and Applications (2021) Let K be a quadratic number field and let \alpha \in K*. We present an explicit finite procedure to compute at once all Kummer degrees [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)] for n,m \geq 1 with n|m ... [more ▼] Let K be a quadratic number field and let \alpha \in K*. We present an explicit finite procedure to compute at once all Kummer degrees [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)] for n,m \geq 1 with n|m, where \zeta_m denotes a primitive m-th root of unity. We can also replace \alpha by any finitely generated subgroup of K*. [less ▲] Detailed reference viewed: 246 (13 UL)![]() Perucca, Antonella ![]() Article for general public (2020) Detailed reference viewed: 103 (6 UL)![]() Perucca, Antonella ![]() Article for general public (2020) Detailed reference viewed: 69 (1 UL)![]() Perucca, Antonella ![]() Article for general public (2020) Detailed reference viewed: 49 (5 UL)![]() Perucca, Antonella ![]() in Rivista di Matematica della Universita di Parma (2020), 11 Detailed reference viewed: 86 (2 UL)![]() Perucca, Antonella ![]() ![]() ![]() in Journal of Number Theory (2020) 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 ▲] Detailed reference viewed: 158 (25 UL)![]() Begalla, Engjell ![]() ![]() Article for general public (2020) Detailed reference viewed: 126 (0 UL)![]() Perucca, Antonella ![]() in Convergence (2020) Detailed reference viewed: 95 (8 UL) |
||