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Rational base number systems for p-adic numbers

Christiane Frougny, Karel Klouda (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.

Rational base number systems for p-adic numbers

Christiane Frougny, Karel Klouda (2012)

RAIRO - Theoretical Informatics and Applications

This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.

Relative Bogomolov extensions

Robert Grizzard (2015)

Acta Arithmetica

A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of K × has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of L × K × . We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.

Représentations cristallines dans le cas d’un corps résiduel imparfait

Olivier Brinon (2006)

Annales de l’institut Fourier

Soit K un corps de valuation discrète complet de caractéristique  0 , dont le corps résiduel k K est de caractéristique p . On suppose que k K admet une p -base finie. Soient K ¯ une clôture algébrique de K et G K = Gal K ¯ / K . On construit et étudie des anneaux de périodes p -adiques B cris B dR qui généralisent ceux définis par J.-M. Fontaine dans le cas où le corps résiduel k K est parfait. Ces anneaux sont munis des structures supplémentaires habituelles ainsi que d’une connexion. Ils permettent d’étendre les notions de représentation...

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