Page 1

Displaying 1 – 9 of 9

Showing per page

Finite and periodic orbits of shift radix systems

Peter Kirschenhofer, Attila Pethő, Paul Surer, Jörg Thuswaldner (2010)

Journal de Théorie des Nombres de Bordeaux

For r = ( r 0 , ... , r d - 1 ) d define the function τ r : d d , z = ( z 0 , ... , z d - 1 ) ( z 1 , ... , z d - 1 , - rz ) , where rz is the scalar product of the vectors r and z . If each orbit of τ r ends up at 0 , we call τ r a shift radix system. It is a well-known fact that each orbit of τ r ends up periodically if the polynomial t d + r d - 1 t d - 1 + + r 0 associated to r is contractive. On the other hand, whenever this polynomial has at least one root outside the unit disc, there exist starting vectors that give rise to unbounded orbits. The present paper deals with the remaining situations of periodicity properties of...

Fonctions digitales le long des nombres premiers

Bruno Martin, Christian Mauduit, Joël Rivat (2015)

Acta Arithmetica

In a recent work we gave some estimations for exponential sums of the form n x Λ ( n ) e x p ( 2 i π ( f ( n ) + β n ) ) , where Λ denotes the von Mangoldt function, f a digital function, and β a real parameter. The aim of this work is to show how these results can be used to study the statistical properties of digital functions along prime numbers.

Currently displaying 1 – 9 of 9

Page 1