Valeur moyenne des fonctions de Piltz sur les entiers sans grand facteur premier
Van der Corput sequences towards general (0,1)–sequences in base b
As a result of recent studies on unidimensional low discrepancy sequences, we can assert that the original van der Corput sequences are the worst distributed with respect to various measures of irregularities of distribution among two large families of –sequences, and even among all –sequences for the star discrepancy . We show in the present paper that it is not the case for the extreme discrepancy by producing two kinds of sequences which are the worst distributed among all –sequences, with...
Van der Corput sets in
In this partly expository paper we study van der Corput sets in , with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for d = 1 by Kamae and M. Mendès France and by Ruzsa, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some...
Vandermonde nets
The second-named author recently suggested identifying the generating matrices of a digital (t,m,s)-net over the finite field with an s × m matrix C over . More exactly, the entries of C are determined by interpreting the rows of the generating matrices as elements of . This paper introduces so-called Vandermonde nets, which correspond to Vandermonde-type matrices C, and discusses the quality parameter and the discrepancy of such nets. The methods that have been successfully used for the investigation...
Verallgemeinerung eines Satzes von Maxfield.
Verallgemeinerung und Anwendungen eines Kusminschen Satzes
Vibrations de classe Cs 2 des tores plats de dimension s et théorie des nombres.
Visible Points on Curves over Finite Fields
For a prime p and an absolutely irreducible modulo p polynomial f(U,V) ∈ ℤ[U,V] we obtain an asymptotic formula for the number of solutions to the congruence f(x,y) ≡ a (mod p) in positive integers x ≤ X, y ≤ Y, with the additional condition gcd(x,y) = 1. Such solutions have a natural interpretation as solutions which are visible from the origin. These formulas are derived on average over a for a fixed prime p, and also on average over p for a fixed integer a.