On the values of a class of analytic functions at algebraic points
On the -expansion of an algebraic number in an algebraic base .
On Thue's theorem.
On two notions of complexity of algebraic numbers
On two theorems of Gelfond and some of their applications
On two theorems of Kopetzky and Schnitzer on the approximation of continued fractions.
On well distribution modulo 1 and systems of numeration
Orbits under algebraic groups and logarithms of algebraic numbers
Ordre de transcendance sur
-adic variant of the convergence Khintchine theorem for curves over
Padé approximations to certain power series.
p-adic logarithmic forms and group varieties II
p-adic polylogarithms and irrationality
p-adic T-numbers do exist
p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.
Padovan and Perrin numbers as products of two generalized Lucas numbers
Let and be the -th Padovan and Perrin numbers respectively. Let be non-zero integers with and , let be the generalized Lucas sequence given by , with and In this paper, we give effective bounds for the solutions of the following Diophantine equations where , and are non-negative integers. Then, we explicitly solve the above Diophantine equations for the Fibonacci, Pell and balancing sequences.
Pair correlation of lattice points with prime constraint
Pairs of additive quadratic forms modulo one
Pairs of polynomials small at a number to certain algebraic powers
Palindromic continued fractions
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 transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.