Displaying similar documents to “On the Euclidean minimum of some real number fields”

The size function h 0 for quadratic number fields

Paolo Francini (2001)

Journal de théorie des nombres de Bordeaux

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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...

Cayley orders

Arjeh M. Cohen, Gabriele Nebe, Wilhelm Plesken (1996)

Compositio Mathematica

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On linear normal lattices configurations

Mordechay B. Levin, Meir Smorodinsky (2005)

Journal de Théorie des Nombres de Bordeaux

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In this paper we extend Champernowne’s construction of normal numbers in base b to the ℤ d case and obtain an explicit construction of the generic point of the ℤ d shift transformation of the set { 0 , 1 , . . . , b - 1 } ℤ d . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base b .