Roberta Centrella (Univ. of Rome 1): Random numbers - theory and
dichotomic generators. 1997.
Original title: Numeri casuali - teoria e generatori dicotomici.
INTRODUCTION

Random and pseudo-random numbers
The linear congruential generator
An inversive congruential generator

EXPONENTIAL SUMS

Characters of finite abelian groups
On the use of characters in number theory
The structure theorem for finite abelian groups
Trace and norm
Trace and norm in finite fields
Additive and multiplicative characters in a finite field
Gauss sums as a connection between the additive and the multiplicative
  characters
The Davenport-Hasse theorem
Character sums with polynomial arguments
Discrepancy bounds: One-dimensional case
Discrepancy bounds in higher dimensions

WALSH FUNCTIONS - HELLEKALEK'S METHOD

The Walsh transformation
Discrepancy bounds in one dimensione
The s-dimensional case

EMPIRICAL TESTS

Other known generators
Comparison by means of Monte Carlo tasks
The test of Kolmogorov-Smirnov
The chi-square test
The serial test
Gap test

EXPERIMENTS

The free semigroup SL(2,N)
Dichotomic generators
Use of the 3x+1 operator as subdivision method
Lindenmayer systems
Dichotomic Lindenmayer systems

Program of the congress in Salzburg (July 1996)

REFERENCES