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