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ORBi

Proportionalitätsrechner für Menschen mit einer Dyskalkulie Perucca, Antonella ; Ronk, Pit Ferdy Scientific Conference (2022) Detailed reference viewed: 43 (9 UL)Der 50cm lange Gliedermaßstab Foyen, Andy ; Perucca, Antonella Scientific Conference (2022) Detailed reference viewed: 56 (4 UL)Geometrie der römischen Mosaiken Perucca, Antonella Scientific Conference (2022) Detailed reference viewed: 29 (0 UL)Visual Mathematical Dictionary Perucca, Antonella Diverse speeches and writings (2022) Detailed reference viewed: 53 (11 UL)Explicit Kummer generators for cyclotomic extensions ; Perucca, Antonella ; Sgobba, Pietro et al in JP Journal of Algebra, Number Theory and Applications (2022) Detailed reference viewed: 129 (16 UL)Minorities in Mathematics Perucca, Antonella Article for general public (2022) Detailed reference viewed: 85 (18 UL)Sharing calculations to understand arithmetical algorithms and parallel computing ; Perucca, Antonella in Mathematics Teacher (2022) Detailed reference viewed: 122 (10 UL)Arithmetic Billiards Perucca, Antonella ; ; Tronto, Sebastiano in Recreational Mathematics Magazine (2022) Detailed reference viewed: 103 (9 UL)How to become the world record holder for solving the Rubik's cube Perucca, Antonella ; Tronto, Sebastiano Speeches/Talks (2021) Detailed reference viewed: 57 (13 UL)Every number is the beginning of a power of 2 Perucca, Antonella Article for general public (2021) Detailed reference viewed: 67 (5 UL)The degree of Kummer extensions of number fields Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano 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: 202 (12 UL)Kummer theory for number fields via entanglement groups Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano in Manuscripta Mathematica (2021) Detailed reference viewed: 153 (6 UL)Explicit Kummer theory for quadratic fields ; Perucca, Antonella ; Sgobba, Pietro et al 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: 267 (13 UL)Staircase numbers Perucca, Antonella Article for general public (2021) Detailed reference viewed: 66 (0 UL)Four points, two distances Perucca, Antonella Article for general public (2020) Detailed reference viewed: 69 (1 UL)The 15 puzzle Perucca, Antonella Article for general public (2020) Detailed reference viewed: 103 (6 UL)The seven bridges of Königsberg Perucca, Antonella Article for general public (2020) Detailed reference viewed: 50 (5 UL)The degree of non-Galois Kummer extensions of number fields Perucca, Antonella in Rivista di Matematica della Universita di Parma (2020), 11 Detailed reference viewed: 87 (2 UL)Addendum to: Reductions of algebraic integers Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano 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: 161 (25 UL)The ABCD of cyclic quadrilaterals Begalla, Engjell ; Perucca, Antonella Article for general public (2020) Detailed reference viewed: 129 (0 UL) |
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