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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…
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…