2 citations · 5 across the 6 of their papers we have counts for
9 papers
A linear independence criterion for -adic Hurwitz zeta values at odd integers
Makoto Kawashima, Anthony Poëls
In this article, a new criterion is established to obtain the linear independence of some values of the -adic Hurwitz zeta function at odd integers . We generalize a th…
On the linear independence of -adic polygamma values
Makoto Kawashima, Anthony Poëls
In this article, we present a new linear independence criterion for values of the -adic polygamma functions defined by J.~Diamond. As an application, we obtain the linear indepe…
-unit equation in two variables and Padé approximations
Noriko Hirata-Kohno, Makoto Kawashima, Anthony Poëls +1
In this article, we use Padé approximations constructed for binomial functions, to give a new upper bound for the number of the solutions of the -unit equation. Combining explic…
Simultaneous rational approximation to successive powers of a real number
Anthony Poëls, Damien Roy
We develop new tools leading, for each integer , to a significantly improved upper bound for the uniform exponent of rational approximation to successive p…
Exponents of Diophantine approximation in dimension two for a general class of numbers
Anthony Poëls
We study the Diophantine properties of a new class of transcendental real numbers which contains, among others, Roy's extremal numbers, Bugeaud-Laurent Sturmian continued fractions…
A class of maximally singular sets for rational approximation
Anthony Poëls
We say that a subset of is maximally singular if its contains points with -linearly independent homogenous coordinates whose uniform exponent…
A new exponent of simultaneous rational approximation
Anthony Poëls
We introduce a new exponent of simultaneous rational approximation for pairs of real numbers , in complement to the classical exponents of bes…
Exponents of diophantine approximation in dimension for numbers of Sturmian type
Anthony Poëls
We generalize the construction of Roy's Fibonacci type numbers to the case of a Sturmian recurrence and we determine the classical exponents of approximation , $\widehatω_2…
The complex case of Schmidt's going-down Theorem
Anthony Poels
In 1967, Schmidt wrote a seminal paper [10] on heights of subspaces of R n or C n defined over a number field K, and diophantine approximation problems. The going-down Theorem -- o…