Multiplication par un entier d'une fraction continue périodique
New criteria for canonical number systems
Nombres algébriques et substitutions
Normal number constructions for Cantor series with slowly growing bases
Let be a sequence of bases with . In the case when the are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose -Cantor series expansion is both -normal and -distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of , and from this construction we can provide computable constructions of numbers with atypical normality properties.
Normal recurring decimals, normal periodic systems, (j,ε) - normality, and normal numbers
Normality of numbers generated by the values of polynomials at primes
Note on Egyptian fractions.
Note on the diophantine equation 1 + x + x2 + ... + xn = ym.
Notes on generalized Dedekind sums
Numeration systems, substitution dynamical systems and Rauzy fractals.
O násobení desetinných čísel
On a conjecture of Dekking : The sum of digits of even numbers
Let and denote by the sum-of-digits function in base . For considerIn 1983, F. M. Dekking conjectured that this quantity is greater than and, respectively, less than for infinitely many , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.
On a problem of Bednarek
We answer a question of Bednarek proposed at the 9th Polish, Slovak and Czech conference in Number Theory.
On a problem of Erdős and Graham concerning digits
On a problem of Frobenius for an almost consecutive set of integers.
On a problem of Tamas Varga
On binary representations of integers with digits .
On expansions of Gaussian integers with non-negative digits.
On Gelfond’s conjecture about the sum of digits of prime numbers
The goal of this paper is to outline the proof of a conjecture of Gelfond [6] (1968) in a recent work in collaboration with Christian Mauduit [11] concerning the sum of digits of prime numbers, reflecting the lecture given in Edinburgh at the Journées Arithmétiques 2007.
On infinite series representations of real numbers