Y. Bugeaud

activity

20032026

most citedRoot separation for irreducible integer polynomials

31 citations · 241 across the 73 of their papers we have counts for

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80 papers · 1 filter

math.NT2026

Refinements of Peck's theorem on simultaneous approximation to algebraic numbers

Yann Bugeaud, Bernard de Mathan

Let $n$ be an integer with $n \geq 2$ , and let $E$ be a real algebraic number field of degree $n + 1$ over $Q$ . Let $α_{1}, \dots, α_{n}$ be real numbers in $E$ such that $(1,α_…

math.NT2026

On the binary representation of powers of $3$

Yann Bugeaud

We establish that only finitely many powers of $3$ can have a simple binary representation.

math.NT2026

On the difference between perfect powers and integral $S$ -units

Yann Bugeaud

Let $q_{1}, \dots, q_{t}$ be distinct prime numbers. Let $a_{1}, \dots, a_{t}$ be nonnegative integers. We establish effective lower bounds for $∣ z^{d} - q_{1}^{a_{1}} \dots q_{t}^{a_{t}} ∣$ and…

math.NT2025

On the irrationality exponent of real numbers with low complexity expansion

Yann Bugeaud, Hajime Kaneko, Dong Han Kim

Let $ξ$ be a real number and $b \geq 2$ an integer. We study the relationship between the irrationality exponent of $ξ$ and the subword complexity $p (n, x)$ of the $b$ -ary…

math.NT2025

On the $b$ -ary expansion of a real number whose irrationality exponent is close to 2

Yann Bugeaud, Dong Han Kim

Let $b \geq 2$ be an integer and $ξ$ an irrational real number. We establishes that, if the irrationality exponent of $ξ$ is less than $2.324 \dots$ , then the $b$ -ary expansion of…

math.NT2025

Simultaneous multiplicative rational approximation to a real and a $p$ -adic numbers

Yann Bugeaud, Bernard de Mathan

We give new examples of pairs composed of a real and a $p$ -adic numbers that satisfy a conjecture on simultaneous multiplicative approximation by rational numbers formulated by Ein…

math.NT2023

Explicit bounds for the solutions of superelliptic equations over number fields

Attila Bérczes, Yann Bugeaud, Kálmán Győry +3

Let $f$ be a polynomial with coefficients in the ring $O_{S}$ of $S$ -integers of a number field $K$ , $b$ a non-zero $S$ -integer, and $m$ an integer $\geq 2$ . We consider the equation…

math.NT2023★ 2 cited

Metrical properties of Hurwitz Continued Fractions

Yann Bugeaud, Gerardo Gonzalez Robert, Mumtaz Hussain

We develop the geometry of Hurwitz continued fractions, a major tool in understanding the approximation properties of complex numbers by ratios of Gaussian integers. Based on a tho…

math.NT2023★ 1 cited

Apollonius circles and the number of irreducible factors of polynomials

Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Yann Bugeaud +2

We provide upper bounds for the sum of the multiplicities of the non-constant irreducible factors that appear in the canonical decomposition of a polynomial $f (X) \in Z [X]$ ,…

math.NT2023

Effective Approximation to Complex Algebraic Numbers by Algebraic Numbers of Bounded Degree

Prajeet Bajpai, Yann Bugeaud

We establish the first effective improvements on the Liouville inequality for approximation to complex non-real algebraic numbers by complex algebraic numbers of degree at most 4.

math.NT2022

Some arithmetical properties of convergents to algebraic numbers

Yann Bugeaud, Khoa D. Nguyen

Let $ξ$ be an irrational algebraic real number and $(p_{k} / q_{k})_{k \geq 1}$ denote the sequence of its convergents. Let $(u_{n})_{n \geq 1}$ be a non-degenerate linear recurrence sequ…

math.NT2022★ 1 cited

$B^{'}$

Yann Bugeaud

Let $n \geq 2$ be an integer and $α_{1}, \dots, α_{n}$ be non-zero algebraic numbers. Let $b_{1}, \dots, b_{n}$ be integers with $b_{n} \neq = 0$ , and set $B = \max\{3, |b_1|, \ldots , |b_n…

math.NT2022

Transcendence and continued fraction expansion of values of Hecke-Mahler series

Yann Bugeaud, Michel Laurent

Let $θ$ and $ρ$ be real numbers with $0 \leq θ, ρ < 1$ and $θ$ irrational. We show that the Hecke-Mahler series $$ F_{θ, ρ} (z_1, z_2) = \sum_{k_1 \ge 1} \, \sum_{k_2 = 1}^{\lfloor k…

math.NT2022

The Thue-Morse continued fractions in characteristic $2$ are algebraic

Yann Bugeaud, Guo-Niu Han

Let $a, b$ be distinct, non-constant polynomials in $F_{2} [z]$ . Let $ξ_{a, b}$ be the power series in $F_{2} ((z^{- 1}))$ whose sequence of partial quotients is the…

math.NT2021

On the rational approximation to $p$ -adic Thue--Morse numbers

Yann Bugeaud

Let $p$ be a prime number and $ξ$ an irrational $p$ -adic number. Its multiplicative irrationality exponent $μ^{\times} (ξ)$ is the supremum of the real numbers $μ^{\times}$ for…

math.NT2021

On the rational approximation to Thue--Morse rational numbers

Yann Bugeaud, Guo-Niu Han

Let $b \geq 2$ and $ℓ \geq 1$ be integers. We establish that there is an absolute real number $K$ such that all the partial quotients of the rational number $$ \prod_{h = 0}^\ell…

math.NT2021★ 1 cited

Multiplicative dependence of rational values modulo approximate finitely generated groups

Attila Bérczes, Yann Bugeaud, Kálmán Győry +3

In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are `close' (with respect to the Weil height) to divisi…

math.NT2021

Classical and uniform exponents of multiplicative $p$ -adic approximation

Yann Bugeaud, Johannes Schleischitz

Let $p$ be a prime number and $ξ$ an irrational $p$ -adic number. Its irrationality exponent $μ (ξ)$ is the supremum of the real numbers $μ$ for which the system of inequalities $$ 0…

math.NT2021★ 1 cited

Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers

Yann Bugeaud, Michel Laurent

Let $θ = [0; a_{1}, a_{2}, \dots]$ be the continued fraction expansion of an irrational real number $θ \in (0, 1)$ . It is well-known that the characteristic Sturmian word of slope $θ$ is…

math.NT2021

Apollonius circles and irreducibility criteria for polynomials

Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Yann Bugeaud +1

We prove the irreducibility of integer polynomials $f (X)$ whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscisae $a$ and $b$ , w…

math.NT2021

Fractional parts of powers of real algebraic numbers

Yann Bugeaud

Let $α$ be a real number greater than $1$ . We establish an effective lower bound for the distance between an integral power of $α$ and its nearest integer.

math.NT2020

Mahler's and Koksma's classifications in fields of power series

Jason Bell, Yann Bugeaud

Let $q$ a prime power and $F_{q}$ the finite field of $q$ elements. We study the analogues of Mahler's and Koksma's classifications of complex numbers for power series in $…

math.NT2020

On simultaneous rational approximation to a $p$ -adic number and its integral powers, II

Dzmitry Badziahin, Yann Bugeaud, Johannes Schleischitz

Let $p$ be a prime number. For a positive integer $n$ and a real number $ξ$ , let $λ_{n} (ξ)$ denote the supremum of the real numbers $λ$ for which there are infinitely many integer t…

math.NT2020

On the Lévy constants of Sturmian continued fractions

Yann Bugeaud, Dong Han Kim, Seul Bee Lee

The Lévy constant of an irrational real number is defined by the exponential growth rate of the sequence of denominators of the principal convergents in its continued fraction expa…

Refinements of Peck's theorem on simultaneous approximation to algebraic numbers

On the binary representation of powers of 3

On the difference between perfect powers and integral S-units

On the irrationality exponent of real numbers with low complexity expansion

On the b-ary expansion of a real number whose irrationality exponent is close to 2

Simultaneous multiplicative rational approximation to a real and a p-adic numbers

Explicit bounds for the solutions of superelliptic equations over number fields

Metrical properties of Hurwitz Continued Fractions

Apollonius circles and the number of irreducible factors of polynomials

Effective Approximation to Complex Algebraic Numbers by Algebraic Numbers of Bounded Degree

Some arithmetical properties of convergents to algebraic numbers

B′

Transcendence and continued fraction expansion of values of Hecke-Mahler series

The Thue-Morse continued fractions in characteristic 2 are algebraic

On the rational approximation to p-adic Thue--Morse numbers

On the rational approximation to Thue--Morse rational numbers

Multiplicative dependence of rational values modulo approximate finitely generated groups

Classical and uniform exponents of multiplicative p-adic approximation

Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers

Apollonius circles and irreducibility criteria for polynomials

Fractional parts of powers of real algebraic numbers

Mahler's and Koksma's classifications in fields of power series

On simultaneous rational approximation to a p-adic number and its integral powers, II

On the Lévy constants of Sturmian continued fractions

On the binary representation of powers of $3$

On the difference between perfect powers and integral $S$ -units

On the $b$ -ary expansion of a real number whose irrationality exponent is close to 2

Simultaneous multiplicative rational approximation to a real and a $p$ -adic numbers

$B^{'}$

The Thue-Morse continued fractions in characteristic $2$ are algebraic

On the rational approximation to $p$ -adic Thue--Morse numbers

Classical and uniform exponents of multiplicative $p$ -adic approximation

On simultaneous rational approximation to a $p$ -adic number and its integral powers, II