Parry expansions of polynomial sequences.
Partitions in the prime number maze
Pattern occurrence in the dyadic expansion of square root of two and an analysis of pseudorandom number generators.
Perfect powers with all equal digits but one.
Periodic expansions and units in quadratic and cubic number fields.
Periods of β-expansions and linear recurrent sequences
Piatetski-Shapiro sequences via Beatty sequences
Integer sequences of the form , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference , which measures the deviation of the mean value of φ on the subsequence from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by attains both of its values with asymptotic...
Picturesque exponential sums. II:
Power Sums of Integers with Missing Digits.
Prime numbers along Rudin–Shapiro sequences
For a large class of digital functions , we estimate the sums (and , where denotes the von Mangoldt function (and the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.
Primes with preassigned digits
Propriétés nouvelles des fractions décimales périodiques
Propriétés q-multiplicatives de la suite , c > 1
Propriétés topologiques et combinatoires des échelles de numération
Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.
Quelques problèmes relatifs à la théorie des fractions continues limitées
Quelques problèmes relatifs à la théorie des fractions continues limitées
Regular maps in generalized number systems
Relations among arithmetical functions, automatic sequences, and sum of digits functions induced by certain Gray codes
In the study of the -adic sum of digits function , the arithmetical function and for plays a very important role. In this paper, we firstly generalize the relation between and to a bijective relation between arithmetical functions. And as an application, we investigate some aspects of the sum of digits functions induced by binary infinite Gray codes . We can show that the difference of the sum of digits function, , is realized by an automaton. And the summation formula of the sum...
Remarks on self-affine tilings.
Representations of real numbers by series of reciprocals of odd integers