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Trigonometry for the multiples of 3 degrees Perucca, Antonella ; Stranen, Deborah E-print/Working paper (2019) Detailed reference viewed: 31 (4 UL)Addendum to: Reductions of algebraic integers Perucca, Antonella ; Sgobba, Pietro ; Tronto, Sebastiano E-print/Working paper (2019) 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: 87 (15 UL)Kummer theory for number fields and the reductions of algebraic numbers Perucca, Antonella ; Sgobba, Pietro E-print/Working paper (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: 122 (28 UL)Het kunstgalerijprobleem Perucca, Antonella Article for general public (2019) Detailed reference viewed: 28 (5 UL)Reductions of elliptic curves Perucca, Antonella in Proceedings of the Roman Number Theory Association (2019), 4 Detailed reference viewed: 77 (7 UL)Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind Perucca, Antonella ; ; in College Mathematics Journal (2018) Detailed reference viewed: 30 (2 UL)Understanding the Babylonian tablet ‘Plimpton 322’ with the decimal system Perucca, Antonella ; E-print/Working paper (2018) Detailed reference viewed: 42 (1 UL)Driehoeken met onderling 5 gelijke zijden en hoeken Perucca, Antonella Article for general public (2018) Detailed reference viewed: 40 (6 UL)The PytEuk puzzle Perucca, Antonella Diverse speeches and writings (2018) We present an original mathematical exhibit. Detailed reference viewed: 44 (10 UL)Math around the Clock Perucca, Antonella Article for general public (2018) This is an article for the general public about mathematical clocks. Several original mathematical clocks are also presented. Detailed reference viewed: 58 (7 UL)Reductions of one-dimensional tori II Perucca, Antonella in Association for Women in Mathematics Series (2018) Detailed reference viewed: 64 (1 UL)Reductions of algebraic integers II Perucca, Antonella in Association for Women in Mathematics Series (2018) Detailed reference viewed: 84 (7 UL)Arithmetic billiards Perucca, Antonella Article for general public (2018) Detailed reference viewed: 38 (5 UL)Reductions of points on algebraic groups ; Perucca, Antonella E-print/Working paper (2017) Detailed reference viewed: 27 (6 UL)Multiplicative order and Frobenius symbol for the reductions of number fields Perucca, Antonella E-print/Working paper (2017) Detailed reference viewed: 60 (5 UL)The 1-eigenspace for matrices in GL2(ℤℓ) ; Perucca, Antonella in New York Journal of Mathematics (2017) Detailed reference viewed: 837 (2 UL)The Chinese Remainder Clock Perucca, Antonella in College Mathematics Journal (2017) Detailed reference viewed: 24 (0 UL)Reductions of one-dimensional tori Perucca, Antonella in International Journal of Number Theory (2017) Detailed reference viewed: 58 (5 UL)Reductions of algebraic integers ; Perucca, Antonella in Journal of Number Theory (2016) Detailed reference viewed: 67 (4 UL)The order of the reductions of an algebraic integer Perucca, Antonella in Journal of Number Theory (2015) Detailed reference viewed: 63 (1 UL) |
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