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The size function h 0 for quadratic number fields

Paolo Francini — 2001

Journal de théorie des nombres de Bordeaux

We study the quadratic case of a conjecture made by Van der Geer and Schoof about the behaviour of certain functions which are defined over the group of Arakelov divisors of a number field. These functions correspond to the standard function h 0 for divisors of algebraic curves and we prove that they reach their maximum value for principal Arakelov divisors and nowhere else. Moreover, we consider a function k 0 ˜ , which is an analogue of exp h 0 defined on the class group, and we show it also assumes its...

Ordinare numeri e ordinare parole

Claudio BernardiPaolo Francini — 2007

Bollettino dell'Unione Matematica Italiana

Vengono descritte varie relazioni che legano l'ordinamento di alcuni simboli base, come cifre o lettere, agli ordinamenti delle sequenze formate da quei simboli, ad esempio numeri o parole. Si esaminano diversi casi, nella pratica matematica e nell'esperienza comune, sul piano teorico e didattico. La situazione presenta vari aspetti più complicati di quanto usualmente si pensi.

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