Noise Oscillators and Algebraic Randomness : From Noise in Communication Systems of Number Theory Lectures of a School Held in Chapelle des Bois France April 5–10 1999 Noise is ubiquitous in nature and in man made systems. Noise in oscillators perturbs high technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum 1 f and phase noise in systems such as electronic amplifiers oscillators and receivers trapped ions cosmic ray showers and in commercial applications. A strong link between 1 f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a School in Chapelle des Bois (Jura France) held from April 6 to 10 1999 by engineers physisicts and mathematicians