Publications (35)
A height gap theorem for coefficients of Mahler functions
Boris Adamczewski, Jason Bell, Daniel Smertnig
We study the asymptotic growth of coefficients of Mahler power series with algebraic coefficients, as measured by their logarithmic Weil height. We show that there are five differe…
Relations algébriques entre valeurs de E-fonctions ou de M-fonctions
Boris Adamczewski, Colin Faverjon
We prove that all algebraic relations over between values of Siegel's -functions at some non-zero algebraic point have a functional source, in that they c…
Mahler's method in several variables I: The theory of regular singular systems
Boris Adamczewski, Colin Faverjon
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two m…
On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited
Boris Adamczewski, Julien Cassaigne, Marion Le Gonidec
We consider the complexity of integer base expansions of algebraic irrational numbers from a computational point of view. We show that the Hartmanis--Stearns problem can be solved…
Algebraic independence and linear difference equations
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin +1
We consider pairs of automorphisms acting on fields of Laurent or Puiseux series: pairs of shift operators , of -di…
On the expansion of some exponential periods in an integer base
Boris Adamczewski
We derive a lower bound for the subword complexity of the base- expansion () of all real numbers whose irrationality exponent is equal to 2. This provides a generalizat…
On vanishing coefficients of algebraic power series over fields of positive characteristic
Boris Adamczewski, Jason P. Bell
Let be a field of characteristic and let be a power series in variables with coefficients in that is algebraic over the field of multivariate rat…
On the Littlewood conjecture in fields of power series
Boris Adamczewski, Yann Bugeaud
Let $\k$ be an arbitrary field. For any fixed badly approximable power series in $\k((X^{-1}))$, we give an explicit construction of continuum many badly approximable power se…
The many faces of the Kempner number
Boris Adamczewski
In this survey, we present five different proofs for the transcendence of Kempner's number, defined by the infinite series . We take the oppo…
A new proof of Nishioka's theorem in Mahler's method
Boris Adamczewski, Colin Faverjon
In a recent work [3], the authors established new results about general linear Mahler systems in several variables from the perspective of transcendental number theory, such as a m…
Méthode de Mahler, transcendance et relations linéaires : aspects effectifs
Boris Adamczewski, Colin Faverjon
This note deals with some effective results in Mahler's method. In a recent work, we used a theorem of Philippon to show that given a Mahler function in , wher…
Rational numbers with purely periodic -expansion
Boris Adamczewski, Christiane Frougny, Anne Siegel +1
We study real numbers with the curious property that the -expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real numb…
Palindromic continued fractions
Boris Adamczewski, Yann Bugeaud
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new t…
Mahler's method in several variables and finite automata
Boris Adamczewski, Colin Faverjon
We develop a theory of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence, which also includes the possibility of dealing w…
Mahler's method in several variables II: Applications to base change problems and finite automata
Boris Adamczewski, Colin Faverjon
This is the second part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. From the lift…
Diophantine properties of real numbers generated by finite automata
Boris Adamczewski, Julien Cassaigne
We study some diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the -ad…
On the Littlewood conjecture in simultaneous Diophantine approximation
Boris Adamczewski, Yann Bugeaud
For any given real number with bounded partial quotients, we construct explicitly continuum many real numbers with bounded partial quotients for which the pair …
A note on Christol's theorem
Boris Adamczewski, Reem Yassawi
Christol's theorem characterises algebraic power series over finite fields in terms of finite automata. In a recent article, Bridy develops a new proof of Christol's theorem by Spe…
Congruences modulo cyclotomic polynomials and algebraic independence for -series
Boris Adamczewski, Jason P. Bell, Ãric Delaygue +1
We prove congruence relations modulo cyclotomic polynomials for multisums of -factorial ratios, therefore generalizing many well-known -Lucas congruences. Such congruences co…
A Liouville-Type Inequality for Values of Mahler M-Functions
Boris Adamczewski, Colin Faverjon
We establish a Liouville-type inequality for the values, at a common nonzero algebraic point, of arbitrary Mahler Mq-functions. As an application, we prove that no such value is a…
On the complexity of algebraic numbers II. Continued fractions
Boris Adamczewski, Yann Bugeaud
The continued fraction expansion of an irrational number is eventually periodic if and only if is a quadratic irrationality. However, very little is known regarding the s…
Bracket words: a generalisation of Sturmian words arising from generalised polynomials
Boris Adamczewski, Jakub Konieczny
Generalised polynomials are maps constructed by applying the floor function, addition, and multiplication to polynomials. Despite superficial similarity, generalised polynomials ex…
Diagonalization and Rationalization of algebraic Laurent series
Boris Adamczewski, Jason P. Bell
We prove a quantitative version of a result of Furstenberg and Deligne stating that the the diagonal of a multivariate algebraic power series with coefficients in a field of positi…
Continued fractions and transcendental numbers
Boris Adamczewski, Yann Bugeaud, Les J. L. Davison
It is widely believed that the continued fraction expansion of every irrational algebraic number either is eventually periodic (and we know that this is the case if and only i…
Exceptional values of E-functions at algebraic points
Boris Adamczewski, Tanguy Rivoal
E-functions are entire functions with algebraic Taylor coefficients satisfying certain arithmetic conditions, and which are also solutions of linear differential equations with rat…
A problem around Mahler functions
Boris Adamczewski, Jason P. Bell
Let be a field of characteristic zero and and be two multiplicatively independent positive integers. We prove the following result that was conjectured by Loxton and va…
Algebraic Independence Measures for Values of E-functions and M-functions
Colin Faverjon, Boris Adamczewski
In this article, we establish a Liouville-type inequality for polynomials evaluated at the values of arbitrary Siegel E-functions at non-zero algebraic points. Additionally, we pro…
Diagonals and algebraicity modulo : a sharper degree bound
Boris Adamczewski, Alin Bostan, Xavier Caruso
In 1984, Deligne proved that for any prime number , the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is algebraic over…
Addendum to: Mahler's method in several variables and finite automata
Colin Faverjon, Boris Adamczewski
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
Hypertranscendence and linear difference equations
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin
After Hölder proved his classical theorem about the Gamma function, there has been a whole bunch of results showing that solutions to linear difference equations tend to be hypert…
On the complexity of algebraic number I. Expansions in integer bases
Boris Adamczewski, Yann Bugeaud
Let be an integer. We prove that the -adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic…
A sharper multivariate Christol's theorem with applications to diagonals and Hadamard products
Boris Adamczewski, Alin Bostan, Xavier Caruso
We provide a new proof of the multivariate version of Christol's theorem about algebraic power series with coefficients in finite fields, as well as of its extension to perfect gro…
(Logarithmic) densities for automatic sequences along primes and squares
Boris Adamczewski, Michael Drmota, Clemens Müllner
In this paper we develop a method to transfer density results for primitive automatic sequences to logarithmic-density results for general automatic sequences. As an application we…
On the Maillet--Baker continued fractions
Boris Adamczewski, Yann Bugeaud
We use the Schmidt Subspace Theorem to establish the transcendence of a class of quasi-periodic continued fractions. This improves earlier works of Maillet and of A. Baker. We also…
Méthode de Mahler: relations linéaires, transcendance et applications aux nombres automatiques
Boris Adamczewski, Colin Faverjon
This paper is concerned with Mahler's method. We study in detail the structure of linear relations between values of Mahler functions at algebraic points. In particular, given a fi…