8 papers
On the binary representation of powers of
Yann Bugeaud
We establish that only finitely many powers of can have a simple binary representation.
On the difference between perfect powers and integral -units
Yann Bugeaud
Let be distinct prime numbers. Let be nonnegative integers. We establish effective lower bounds for and…
On the -ary expansion of a real number whose irrationality exponent is close to 2
Yann Bugeaud, Dong Han Kim
Let be an integer and an irrational real number. We establishes that, if the irrationality exponent of is less than , then the -ary expansion o…
On the irrationality exponent of real numbers with low complexity expansion
Yann Bugeaud, Hajime Kaneko, Dong Han Kim
Let be a real number and an integer. We study the relationship between the irrationality exponent of and the subword complexity of the -ar…
On the conjugates of Christoffel words
Y. Bugeaud, C. Reutenauer
We introduce a parametrization of the conjugates of Christoffel words based on the integer Ostrowski numeration system. We use it to give a precise description of the borders (pref…
Simultaneous multiplicative rational approximation to a real and a -adic numbers
Yann Bugeaud, Bernard de Mathan
We give new examples of pairs composed of a real and a -adic numbers that satisfy a conjecture on simultaneous multiplicative approximation by rational numbers formulated by Ein…