Automata in Number Theory

Project Information

ANT

Grant agreement ID: 648132

DOI

10.3030/648132

Project closed

EC signature date 10 September 2015

Start date 1 October 2015

End date 31 March 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 438 745,00

EU contribution

€ 1 438 745,00

Coordinated by

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (9)

Mahler's method in several variables and finite automata

Author(s): Adamczewski, Boris; Faverjon, Colin
Published in: ArXIv, Issue 3, 2020
Publisher: ArXiv

A NOTE ON CHRISTOL'S THEOREM

Author(s): Adamczewski, Boris; Yassawi, Reem
Published in: https://hal.archives-ouvertes.fr/hal-02161492, Issue 5, 2019
Publisher: ArXiv

Gowers norms for automatic sequences

Author(s): Byszewski, Jakub; Konieczny, Jakub; Müllner, Clemens
Published in: ArXiv, Issue 4, 2020
Publisher: ArXiv

"Maximal Unipotent Monodromy, congruences ""\`a la Lucas"" and Algebraic independence"

Author(s): Montoya, Daniel Vargas
Published in: Issue 5, 2021
Publisher: Arxiv

Some supercongruences of arbitrary length

Author(s): Beukers, Frits; Delaygue, Eric
Published in: https://hal.archives-ouvertes.fr/hal-02091737, Issue 1, 2020
Publisher: HAL

Mahler's method in several variables II: Applications to base change problems and finite automata

Author(s): Boris Adamczewski and Colin Faverjon
Published in: 2018
Publisher: arXiv

Mahler's method in several variables I: The theory of regular singular systems

Author(s): Boris Adamczewski and Colin Faverjon
Published in: 2018
Publisher: arXiv

Some supercongruences of arbitrary length

Author(s): Beukers, Frits; Delaygue, Eric
Published in: Issue 2, 2018
Publisher: arXiv

An algorithm to determine regular singular Mahler systems

Author(s): Faverjon, Colin; Poulet, Marina
Published in: https://hal.archives-ouvertes.fr/hal-03147365, Issue 4, 2021
Publisher: HAL

Book chapters (2)

Automata in number theory

Author(s): Adamczewski, Boris; Bell, Jason,
Published in: Handbook of automata theory. Vol. II. Automata in mathematics and selected applications, Issue 13, 2021
Publisher: European Mathematical Society
DOI: 10.4171/automata-1/25

On the Kernel curves associated with walks in the quarter plane

Author(s): Dreyfus, Thomas; Hardouin, Charlotte; Roques, Julien; Singer, Michael F.
Published in: Transcendence in algebra, combinatorics, geometry and number theory, Issue 2, 2021
Publisher: Springer Cham.
DOI: 10.1007/978-3-030-84304-5\_3

Peer reviewed articles (40)

Automatic sequences are orthogonal to aperiodic multiplicative functions

Author(s): Mariusz Lemańczyk; Clemens Müllner
Published in: Discrete Contin. Dyn. Syst., Issue 5, 2020, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2020260

On primary pseudo-polynomials (around Ruzsa’s conjecture)

Author(s): É. Delaygue; T. Rivoal
Published in: International Journal of Number Theory, Issue 5, 2022, ISSN 1793-0421
Publisher: World Scientific Publishing Co
DOI: 10.1142/s1793042122500828

Automorphisms of automatic shifts

Author(s): Clemens Müllner; Reem Yassawi
Published in: Ergodic Theory and Dynamical Systems, Issue 1, 2021, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2020.13

A sum-shuffle formula for zeta values in Tate algebras

Author(s): Federico Pellarin
Published in: Journal de Théorie des Nombres de Bordeaux, Issue 4, 2017, ISSN 1246-7405
Publisher: Universite de Bordeaux III
DOI: 10.5802/jtnb.1010

Walks in the quarter plane: Genus zero case

Author(s): Thomas Dreyfus; Charlotte Hardouin; Julien Roques; Michael F. Singer
Published in: Journal of Combinatorial Theory. Series A, Issue 2, 2020, ISSN 0097-3165
Publisher: Academic Press
DOI: 10.1016/j.jcta.2020.105251

Topological rigidity of linear cellular automaton shifts

Author(s): Robbert Fokkink; Robbert Fokkink; Reem Yassawi; Reem Yassawi
Published in: Indag. Math., Issue 2, 2018, ISSN 0019-3577
Publisher: Elsevier BV
DOI: 10.1016/j.indag.2018.05.011

Hypertranscendence of solutions of Mahler equations

Author(s): Thomas Dreyfus; Charlotte Hardouin; Julien Roques
Published in: Journal of the European Mathematical Society, Issue 4, 2018, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/810

The Ellis semigroup of bijective substitutions

Author(s): Kellendonk, Johannes; Yassawi, Reem
Published in: Groups, Geometry, and Dynamics, Issue 1, 2022, ISSN 1661-7207
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/ggd/640

Randomness and non-randomness properties of Piatetski-Shapiro sequences modulo m

Author(s): Jean-Marc Deshouillers; Michael Drmota; Clemens Müllner; Lukas Spiegelhofer
Published in: Mathematika, Issue 1, 2019, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/s0025579319000287

M\'ethode de Mahler, transcendance et relations lin\'eaires : aspects effectifs

Author(s): Adamczewski, Boris; Faverjon, Colin
Published in: Journal de Théorie des Nombres de Bordeaux, Issue 1, 2018, ISSN 1246-7405
Publisher: Universite de Bordeaux III

Regular extensions and algebraic relations between values of Mahler functions in positive characteristic

Author(s): Gwladys Fernandes
Published in: Transactions of the American Mathematical Society, Issue 1, 2019, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7798

Mahler's method

Author(s): Adamczewski, Boris
Published in: Documenta Mathematica, Issue 7, 2019, ISSN 1431-0635
Publisher: Deutsche Mathematiker-Vereinigung
DOI: 10.25537/dm.2019.sb-95-122

ALGEBRAIC INDEPENDENCE AND LINEAR DIFFERENCE EQUATIONS

Author(s): Adamczewski, Boris; Dreyfus, Thomas; Hardouin, Charlotte; Wibmer, Michael
Published in: Journal of the European Mathematical Society, Issue 5, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House

Logarithmic) densities for automatic sequences along primes and squares

Author(s): Boris Adamczewski; Michael Drmota; Clemens Müllner
Published in: Transactions of the American Mathematical Society, Issue 5, 2022, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8476

Multiplicative automatic sequences

Author(s): Jakub Konieczny; Mariusz Lemańczyk; Clemens Müllner
Published in: Mathematische Zeitschrift, Issue 5, 2022, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-021-02834-3

On a variant of Schanuel conjecture for the Carlitz exponential

Author(s): Federico Pellarin
Published in: Journal de Théorie des Nombres de Bordeaux, Issue 2, 2017, ISSN 1246-7405
Publisher: Universite de Bordeaux III
DOI: 10.5802/jtnb.1004

Hypertranscendence and linear difference equations

Author(s): Boris Adamczewski; Thomas Dreyfus; Charlotte Hardouin
Published in: Journal of the American Mathematical Society, Issue 5, 2021, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/960

Computing the Lie algebra of the differential Galois group: the reducible case

Author(s): Thomas Dreyfus; Jacques-Arthur Weil
Published in: Crossref, Issue 5, 2022, ISSN 0747-7171
Publisher: Academic Press
DOI: 10.1016/j.jsc.2022.01.006

On the multiple-scale analysis for some linear partial $q$-difference and differential equations with holomorphic coefficients

Author(s): Dreyfus, Thomas; Lastra, Alberto; Malek, Stéphane
Published in: Advances in Difference Equations, Issue 1, 2019, ISSN 1687-1839
Publisher: Hindawi Publishing Corporation
DOI: 10.1186/s13662-019-2263-5

Computing Bugeaud's solutions of q-difference equations with a q-Borel-Laplace summation

Author(s): Dreyfus, Thomas; Eloy, Anton
Published in: "Journal of Difference Equations and Applications, Taylor & Francis, 2016, 22 (10), pp.1501-1511. ⟨10.1080/10236198.2016.1209192⟩", Issue 5, 2016, ISSN 1023-6198
Publisher: Taylor & Francis
DOI: 10.1080/10236198.2016.1209192

Vectorial Drinfeld modular forms over Tate algebras

Author(s): Federico Pellarin; Rudolph Perkins
Published in: International Journal of Number Theory, Issue 1, 2018, ISSN 1793-0421
Publisher: World Scientific Publishing Co
DOI: 10.1142/s1793042118501063

Automaticity and Invariant Measures of Linear Cellular Automata

Author(s): Eric Rowland; Reem Yassawi
Published in: https://hal.archives-ouvertes.fr/hal-02086887, Issue 4, 2020, ISSN 0008-414X
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008414x19000488

Méthode de Mahler en caractéristique non nulle : un analogue du Théorème de Ku. Nishioka

Author(s): Gwladys Fernandes
Published in: Annales de l'Institut Fourier, Issue 1, 2018, ISSN 0373-0956
Publisher: Association des Annales de I'Institut Fourier
DOI: 10.5802/aif.3216

Functional relations for solutions of q-difference equations

Author(s): Thomas Dreyfus; Charlotte Hardouin; Julien Roques
Published in: Mathematische Zeitschrift, Issue 2, 2021, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-020-02669-4

Real difference Galois theory

Author(s): Thomas Dreyfus
Published in: Proceedings of the American Mathematical Society, 2018, Page(s) 1, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/13696

Séminaire Lotharingien de Combinatoire, 78B.54 (2017), 12 pp.

Author(s): Boris Adamczewski, Jason P. Bell, Eric Delaygue,and Frédéric Jouhet
Published in: Séminaire Lotharingien de Combinatoire, Issue 78B.54, 2017, ISSN 1286-4889
Publisher: Séminaire Lotharingien de Combinatoire

Isomonodromic deformation of $q$-difference equations and confluence

Author(s): Thomas Dreyfus
Published in: Proceedings of the American Mathematical Society, Issue 145/3, 2017, Page(s) 1109-1120, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/13173

q -Borel-Laplace summation for q –difference equations with two slopes

Author(s): Thomas Dreyfus, Anton Eloy
Published in: Journal of Difference Equations and Applications, Issue 22/10, 2016, Page(s) 1501-1511, ISSN 1023-6198
Publisher: Taylor & Francis
DOI: 10.1080/10236198.2016.1209192

A problem about Mahler functions

Author(s): Boris Adamczewski and Jason Bell
Published in: Ann. Sc. Norm. Super. Pisa, Issue XVII, 2017, Page(s) 1-55, ISSN 0391-173x
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.201606_010

Méthode de Mahler : relations linéaires, transcendance et applications aux nombres automatiques

Author(s): Boris Adamczewski, Colin Faverjon
Published in: Proceedings of the London Mathematical Society, Issue 115/1, 2017, Page(s) 55-90, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12038

Arithmetic properties of Apéry-like numbers

Author(s): É. Delaygue
Published in: Compositio Mathematica, Issue 154/02, 2018, Page(s) 249-274, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x17007552

Exceptional values of E-functions at algebraic points

Author(s): Boris Adamczewski, Tanguy Rivoal
Published in: Bulletin of the London Mathematical Society, 2018, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.12168

Computing solutions of linear Mahler equations

Author(s): Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, Marc Mezzarobba
Published in: Mathematics of Computation, 2018, Page(s) 1, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3359

A note on certain representations in characteristic p and associated functions

Author(s): F. Pellarin
Published in: Journal of Number Theory, Issue 176, 2017, Page(s) 420-438, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2016.12.001

On the nature of the generating series of walks in the quarter plane

Author(s): Thomas Dreyfus; Charlotte Hardouin; Julien Roques; Michael F. Singer
Published in: Inventiones Mathematicae, Issue 5, 2018, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-018-0787-z

A height gap theorem for coefficients of Mahler functions

Author(s): Adamczewski, Boris; Bell, Jason; Smertnig, Daniel
Published in: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, Issue 5, 2022, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1244

Anderson-Stark units for ${\mathbb F}_{q}[\theta ]$

Author(s): Bruno Anglès; Federico Pellarin; Floric Tavares Ribeiro
Published in: Transactions of the American Mathematical Society, Issue 5, 2018, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/6994

On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited

Author(s): Boris Adamczewski; Julien Cassaigne; Marion Le Gonidec
Published in: 2018, Issue 2, 2019, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7915

"Algebraic independence of $G$-functions and congruences ""à la Lucas""."

Author(s): Boris Adamczewski; Jason P. Bell; Eric Delaygue
Published in: Annales Scientifiques de l'École Normale Supérieure, Issue 4, 2019, ISSN 0012-9593
Publisher: Elsevier BV
DOI: 10.24033/asens.2392

Alg\'ebricit\'e modulo p, s\'eries hyperg\'eom\'etriques et structures de Frobenius forte

Author(s): Montoya, Daniel Vargas
Published in: Bull. Soc. Math. France, Issue 1, 2021, ISSN 0037-9484
Publisher: Societe Mathematique de France
DOI: 10.24033/bsmf.2834