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Converting the Old Babylonian Tablet ‘Plimpton 322’ into the Decimal System as a Classroom Exercise Perucca, Antonella ; in Convergence (2020) Detailed reference viewed: 101 (8 UL)The ABCD of cyclic quadrilaterals Begalla, Engjell ; Perucca, Antonella Article for general public (2020) Detailed reference viewed: 129 (0 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 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)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)Multisets in arithmetics Perucca, Antonella in Multimengen in der Arithmetik (2019) Detailed reference viewed: 38 (1 UL)Trigonometry for the multiples of 3 degrees Perucca, Antonella ; Stranen, Deborah Article for general public (2019) Detailed reference viewed: 63 (8 UL)The Art Gallery Problem Perucca, Antonella Article for general public (2019) Detailed reference viewed: 64 (9 UL)Reductions of points on algebraic groups ; Perucca, Antonella in Journal of the Institute of Mathematics of Jussieu (2019) Detailed reference viewed: 80 (6 UL)Multiplicative order and Frobenius symbol for the reductions of number fields Perucca, Antonella in Research Directions in Number Theory, Association for Women in Mathematics, Series 19 (2019) (2019) Detailed reference viewed: 107 (6 UL)Reductions of elliptic curves Perucca, Antonella in Proceedings of the Roman Number Theory Association (2019), 4 Detailed reference viewed: 115 (9 UL)Kummer theory for number fields and the reductions of algebraic numbers Perucca, Antonella ; Sgobba, Pietro in International Journal of Number Theory (2019) For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov-Ribet method) of the fact that if G is ... [more ▼] For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov-Ribet method) of the fact that if G is a finitely generated and torsion-free multiplicative subgroup of a number field K having rank r, then the ratio between n^r and the Kummer degree [K(\zeta_n,\sqrt[n]{G}):K(\zeta_n)] is bounded independently of n. We then apply this result to generalise to higher rank a theorem of Ziegler from 2006 about the multiplicative order of the reductions of algebraic integers (the multiplicative order must be in a given arithmetic progression, and an additional Frobenius condition may be considered). [less ▲] Detailed reference viewed: 279 (42 UL)The problem of detecting linear dependence Perucca, Antonella in Rivista di Matematica della Universita di Parma (2019) Detailed reference viewed: 100 (14 UL)Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind Perucca, Antonella ; ; in College Mathematics Journal (2018) Detailed reference viewed: 76 (3 UL)Arithmetic billiards Perucca, Antonella Article for general public (2018) Detailed reference viewed: 78 (7 UL)Reductions of algebraic integers II Perucca, Antonella in Association for Women in Mathematics Series (2018) Detailed reference viewed: 127 (7 UL)Reductions of one-dimensional tori II Perucca, Antonella in Association for Women in Mathematics Series (2018) Detailed reference viewed: 113 (1 UL)Driehoeken met onderling 5 gelijke zijden en hoeken Perucca, Antonella ; Article for general public (2018) Detailed reference viewed: 60 (7 UL) |
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