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Automata in Number Theory

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Publications

Hypertranscendence of solutions of Mahler equations

Author(s): Thomas Dreyfus, Charlotte Hardouin, Julien Roques
Published in: To appear in JEMS, 2016

Twofold q-Gevrey asymptotics for linear singularly perturbed q-difference-differential equations with polynomial coefficients

Author(s): Thomas Dreyfus, Alberto Lastra, Stéphane Malek
Published in: 2017

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

Author(s): Boris Adamczewski, Julien Cassaigne, Marion LeGonidec
Published in: 2016

Walks in the quarter plane, genus zero case

Author(s): Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer
Published in: 2017

Functional relations of solutions of q-difference equations

Author(s): Thomas Dreyfus, Charlotte Hardouin, Julien Roques
Published in: 2016

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

Author(s): Boris Adamczewski, Eric Delaygue, and Jason Bell
Published in: To appear in Ann. Sci. Éc. Norm. Supér., 2016

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: To appear in Invent. Math., 2017

Méthode de Mahler, transcendance et relations linéaires : aspects effectifs

Author(s): Boris Adamczewski and Colin Faverjon
Published in: To appear in J. Théor. Nombres Bordeaux, 2016

M\'ethode de Mahler en caract{\'e}ristique non nulle : un analogue du Th\'eor\`eme de Ku. Nishioka

Author(s): Fernandes, Gwladys
Published in: To appear in Ann. Inst. Fourier, Issue 5, 2018

A sum-shuffle formula for zeta values in Tate algebras

Author(s): Pellarin, Federico
Published in: To appear in J. Théor. Nombres Bordeaux, Issue 2, 2018

On a variant of Schanuel conjecture for the Carlitz exponential

Author(s): Pellarin, F
Published in: To appear in J. theory. Nombres Bordeaux, Issue 1, 2018

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

Author(s): Fernandes, Gwladys
Published in: 2018

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

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

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

Some supercongruences of arbitrary length

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

Real difference Galois theory

Author(s): Thomas Dreyfus
Published in: Proceedings of the American Mathematical Society, 2018, Page(s) 1, ISSN 0002-9939
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

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
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
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
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
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
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
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
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
DOI: 10.1016/j.jnt.2016.12.001