Gregory V. Chudnovsky - Böcker

This volume marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Beginning in 1982, the NYNTS has tried to present a broad spectrum of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The list of seminar speakers includes not only Fields Medallists and other established researchers, but also many other younger and less well known mathematicians whose theorems are significant and whose work may become the next big thing in number theory.

This volume is dedicated to Harvey Cohn, Distinguished Professor Emeritus of Mathematics at City College (CUNY). Harvey was one of the organizers of the New York Number Theory Seminar, and was deeply involved in all aspects of the Seminar from its first meeting in January, 1982, until his retirement in December, 1995. We wish him good health and continued hapiness and success in mathematics. The papers in this volume are revised and expanded versions of lectures delivered in the New York Number Theory Seminar. The Seminar meets weekly at the Graduate School and University Center of the City University of New York (CUNY). In addition, some of the papers in this book were presented at a conference on Combinatorial Number Theory that the New York Number Theory Seminar organized at Lehman College (CUNY). Here is a short description of the papers in this volume. The paper of R. T. Bumby focuses on "elementary" fast algorithms in sums of two and four squares. The actual talk had been accompanied by dazzling computer demonstrations. The detailed review of H. Cohn describes the construction of modular equations as the basis of studies of modular forms in the one-dimensional and Hilbert cases.

On the solution of an optimal search problem with an exponential detection function. Covers one- and two-sided detection problems by furnishing continuous and discret time strategies; examines two-sided search strategies with solutions in hide and seek games in many discrete and continuous bounded

Providing immediate access to modern search theory, state-of-the-art methods, related areas of mathematics and their techniques, and applications, this important reference surveys classical results and approaches to search theory as well as the latest procedures of optimal and nearly optimal search planning for the most detailed and comprehensive source on the subject. Search Theory clearly describes the solution of an optimal search problem with an exponential detection function...covers one-and two-sided detection problems by furnishing continuous and discrete time strategies...examines two-sided search strategies with solutions in "hide and seek" games in many discrete and continuous bounded and unbounded domanins...presents a consistent framework for solving complex problems in a unified way by differential equations...discusses systematic means of generating tours for optimal search in bounded domains...and considers a novel class of random search plans.

This is the third Lecture Notes volume to be produced in the framework of the New York Number Theory Seminar. The papers contained here are mainly research papers. N