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Automatic sequences along squares and primes Drmota, Michael | CIRM

Single angle

V

Research talks

Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they are definitely no "quasi-random" sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjectured that the resulting sequences are normal sequences which could be already proved for the Thue-Morse sequence along the subsequence of squares.
This kind of research is very challenging and was mainly motivated by the Gelfond problems for the sum-of-digits function. In particular during the last few years there was a spectacular progress due to the Fourier analytic method by Mauduit and Rivat. In this talk we survey some of these recent developments. In particular we present a new result on subsequences along primes of so-called invertible automatic sequences.
Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they are definitely no "quasi-random" sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjectured that the resulting sequences are normal ...

11B85

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Domaine
Codes MSC

Ressources Electroniques

Books & Print journals

Recherche avancée


0
Z
class="details">Ouvrage

V

- 318 p.
ISBN 978-0-8218-3387-2

Mathematical surveys and monographs , 0104

Localisation : Collection 1er étage

théorie des nombres # suite définie par récurrence # recurrence # suite automatique # courbe elliptique # distribution modulo 1 # nombre pseudo-alléatoire # cryptographie # somme exponentielle # automate cellulaire

11B37 ; 11B85 ; 11G05 ; 11J71 ; 11K45 ; 11T23 ; 37B15 ; 94A60

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Iterated function systems and permutation representations of the cuntz algebra Bratteli, Ola ; Jorgensen, Palle E. T. | American Mathematical Society 1999

Ouvrage

V


ISBN 978-0-8218-0962-4

Memoirs of the american mathematical society , 0663

Localisation : Collection 1er étage

C-algébre # analyse de Fourier # espace d'Hilbert # representation des groupes

11B85 ; 42C05 ; 46L55 ; 47C15

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Automatic sequences:
theory, applications, generalizations
Allouche, Jean-Paul ; Shallit, Jeffrey | Cambridge University Press 2003

Ouvrage

V

- xvi; 571 p.
ISBN 978-0-521-82332-6

Localisation : Ouvrage RdC (ALLO)

suite automatique # théorie des nombres # combinatoire des mots # automate # morphisme uniforme # langage formel

11B85 ; 11-01 ; 68R15 ; 68Q45

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Automatic sequences Von Haeseler, Friedrich | Walter De Gruyter 2003

Ouvrage

V

- 191 p.
ISBN 978-3-11-015629-4

De Gruyter expositions in mathematics , 0036

Localisation : Ouvrage RdC (HAES)

théorie des nombres # série automatique # automate # langage formel # combinatoire des mots # groupe d'Heisenberg # équation de Mahler # suite de Thue-Morse

11B85 ; 68R15

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Algebraic combinatorics on words Lothaire, M. | Cambridge University Press 2002

Ouvrage

V

- xiii; 504 p.
ISBN 978-0-521-18071-9

Encyclopedia of mathematics and its applications , 0090

Localisation : Collection 1er étage

combinatoire des mots # algèbre combinatoire

68R15 ; 68-02 ; 11B85

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