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ANT SIGNED

Automata in Number Theory

Total Cost €

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EC-Contrib. €

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Partnership

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 ANT project word cloud

Explore the words cloud of the ANT project. It provides you a very rough idea of what is the project "ANT" about.

arithmetics    abelian    trivial    prevails    seem    equations    lie    natural    guideline    link    mainly    chaos    enumerative    first    theoretical    complexity    point    powerful    view    somewhere    structures    integers    methodology    baffled    generating    generally    linear    science    language    computer    fractal    directions    last    finitely    ant    concerning    heart    parsing    sequences    theory    rigidity    nature    questions    digital    provides    base    glance    fundamental    few    renewed    constants    stress    combinatorics    positive    representations    decades    international    arithmetical    ordered    placing    mathematicians    serve    formal    expansions    outline    synergy    integer    subject    symbols    monoids    fact    surprisingly    primary    groups    finite    periodic    decidability    ground    lines    opportunity    automatic    automata    recognizing    create    respects    necessarily    differential    objects    breaking    unrelated    interactions    practical    team   

Project "ANT" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Project website https://sites.google.com/site/ercantunivlyon1/home
 Total cost 1˙438˙745 €
 EC max contribution 1˙438˙745 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2015
 Duration (year-month-day) from 2015-10-01   to  2020-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙438˙745.00

Map

 Project objective

Finite automata are fundamental objects in Computer Science, of great importance on one hand for theoretical aspects (formal language theory, decidability, complexity) and on the other for practical applications (parsing). In number theory, finite automata are mainly used as simple devices for generating sequences of symbols over a finite set (e.g., digital representations of real numbers), and for recognizing some sets of integers or more generally of finitely generated abelian groups or monoids. One of the main features of these automatic structures comes from the fact that they are highly ordered without necessarily being trivial (i.e., periodic). With their rich fractal nature, they lie somewhere between order and chaos, even if, in most respects, their rigidity prevails. Over the last few years, several ground-breaking results have lead to a great renewed interest in the study of automatic structures in arithmetics.

A primary objective of the ANT project is to exploit this opportunity by developing new directions and interactions between automata and number theory. In this proposal, we outline three lines of research concerning fundamental number theoretical problems that have baffled mathematicians for decades. They include the study of integer base expansions of classical constants, of arithmetical linear differential equations and their link with enumerative combinatorics, and of arithmetics in positive characteristic. At first glance, these topics may seem unrelated, but, surprisingly enough, the theory of finite automata will serve as a natural guideline. We stress that this new point of view on classical questions is a key part of our methodology: we aim at creating a powerful synergy between the different approaches we propose to develop, placing automata theory and related methods at the heart of the subject. This project provides a unique opportunity to create the first international team focusing on these different problems as a whole.

 Publications

year authors and title journal last update
List of publications.
2018 Pellarin, F
On a variant of Schanuel conjecture for the Carlitz exponential
published pages: , ISSN: , DOI:
To appear in J. theory. Nombres Bordeaux 1 2019-06-06
2017 F. Pellarin
A note on certain representations in characteristic p and associated functions
published pages: 420-438, ISSN: 0022-314X, DOI: 10.1016/j.jnt.2016.12.001
Journal of Number Theory 176 2019-06-06
2018 Boris Adamczewski, Tanguy Rivoal
Exceptional values of E-functions at algebraic points
published pages: , ISSN: 0024-6093, DOI: 10.1112/blms.12168
Bulletin of the London Mathematical Society 2019-06-06
2017 Thomas Dreyfus, Alberto Lastra, Stéphane Malek
Twofold q-Gevrey asymptotics for linear singularly perturbed q-difference-differential equations with polynomial coefficients
published pages: , ISSN: , DOI:
2019-06-06
2018 Fernandes, Gwladys
M\'ethode de Mahler en caract{\'e}ristique non nulle : un analogue du Th\'eor`eme de Ku. Nishioka
published pages: , ISSN: , DOI:
To appear in Ann. Inst. Fourier 5 2019-06-06
2018 Pellarin, Federico
A sum-shuffle formula for zeta values in Tate algebras
published pages: , ISSN: , DOI:
To appear in J. Théor. Nombres Bordeaux 2 2019-06-06
2017 Boris Adamczewski and Jason Bell
A problem about Mahler functions
published pages: 1-55, ISSN: 0391-173x, DOI: 10.2422/2036-2145.201606_010
Ann. Sc. Norm. Super. Pisa XVII 2019-06-06
2016 Boris Adamczewski and Colin Faverjon
Méthode de Mahler, transcendance et relations linéaires : aspects effectifs
published pages: , ISSN: , DOI:
To appear in J. Théor. Nombres Bordeaux 2019-06-06
2017 Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer
Walks in the quarter plane, genus zero case
published pages: , ISSN: , DOI:
2019-06-06
2016 Boris Adamczewski, Eric Delaygue, and Jason Bell
\"Algebraic independence of G-functions and congruences \"\"à la Lucas\"\"\"
published pages: , ISSN: , DOI:
To appear in Ann. Sci. Éc. Norm. Supér. 2019-06-06
2016 Thomas Dreyfus, Charlotte Hardouin, Julien Roques
Hypertranscendence of solutions of Mahler equations
published pages: , ISSN: , DOI:
To appear in JEMS 2019-06-06
2018 Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, Marc Mezzarobba
Computing solutions of linear Mahler equations
published pages: 1, ISSN: 0025-5718, DOI: 10.1090/mcom/3359
Mathematics of Computation 2019-06-06
2017 Boris Adamczewski, Colin Faverjon
Méthode de Mahler : relations linéaires, transcendance et applications aux nombres automatiques
published pages: 55-90, ISSN: 0024-6115, DOI: 10.1112/plms.12038
Proceedings of the London Mathematical Society 115/1 2019-06-06
2016 Boris Adamczewski, Julien Cassaigne, Marion LeGonidec
On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited
published pages: , ISSN: , DOI:
2019-06-06
2017 Boris Adamczewski, Jason P. Bell, Eric Delaygue,and Frédéric Jouhet
Séminaire Lotharingien de Combinatoire, 78B.54 (2017), 12 pp.
published pages: , ISSN: 1286-4889, DOI:
Séminaire Lotharingien de Combinatoire 78B.54 2019-06-06
2018 Thomas Dreyfus
Real difference Galois theory
published pages: 1, ISSN: 0002-9939, DOI: 10.1090/proc/13696
Proceedings of the American Mathematical Society 2019-06-06
2018 É. Delaygue
Arithmetic properties of Apéry-like numbers
published pages: 249-274, ISSN: 0010-437X, DOI: 10.1112/s0010437x17007552
Compositio Mathematica 154/02 2019-06-06
2017 Thomas Dreyfus
Isomonodromic deformation of $q$-difference equations and confluence
published pages: 1109-1120, ISSN: 0002-9939, DOI: 10.1090/proc/13173
Proceedings of the American Mathematical Society 145/3 2019-06-06
2017 Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F. Singer
On the nature of the generating series of walks in the quarter plane
published pages: , ISSN: , DOI:
To appear in Invent. Math. 2019-06-06
2016 Thomas Dreyfus, Charlotte Hardouin, Julien Roques
Functional relations of solutions of q-difference equations
published pages: , ISSN: , DOI:
2019-06-06
2018 Fernandes, Gwladys
Regular extensions and algebraic relations between values of Mahler functions in positive characteristic
published pages: , ISSN: , DOI:
2019-04-18
2018 Boris Adamczewski and Colin Faverjon
Mahler\'s method in several variables II: Applications to base change problems and finite automata
published pages: , ISSN: , DOI:
2019-04-18
2018 Boris Adamczewski and Colin Faverjon
Mahler\'s method in several variables I: The theory of regular singular systems
published pages: , ISSN: , DOI:
2019-04-18
2018 Beukers, Frits; Delaygue, Eric
Some supercongruences of arbitrary length
published pages: , ISSN: , DOI:
2 2019-04-18

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