One of the first concepts one meets in elementary number theory is that of the multiplicative
order. We give a survey of the literature on this topic emphasizing the Artin primitive root …

The book introduces new techniques that imply rigorous lower bounds on the com plexity of
some number-theoretic and cryptographic problems. It also establishes certain attractive …

In this paper we construct a sequence of eigenfunctions of the``quantum Arnold's cat
map''that, in the semiclassical limit, shows a strong scarring phenomenon on the periodic …

We review recent studies on the resonance spectrum of quantum scattering systems, in the
semiclassical limit and assuming chaotic classical dynamics. Stationary quantum properties …

Operators in ergodic spin chains are found to grow according to hydrodynamical equations
of motion. The study of such operator spreading has aided our understanding of many-body …

In this contribution we will review the basic mathematical aspects of quantum maps. Here is
a brief outline of the topics covered in this contribution. Most of the material comes from …

We study the behavior of the greatest common divisor of a^ k-1 and b^ k-1, where a, b are
fixed integers or polynomials, and k varies. In the integer case, we conjecture that when a …

We present one aspect of “Quantum Chaos”, namely the description of high frequency
eigenmodes of a quantum system, the classical limit of which is chaotic (we call such …

It is well known in Kähler geometry that the infinite-dimensional symmetric space of smooth
Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated …

We consider the periods of the linear congruential and the power generators modulo $ n $
and, for fixed choices of initial parameters, give lower bounds that hold for``most''$ n $ when …