Automata in Number Theory

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

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

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.283

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