Number Theory New York Seminar 2003 [Paperback]

This volume of new research papers marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Since 1982, NYNTS has presented a range of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The speakers have included Field medalists as well as promising lesser known mathematicians whose theorems are significant. The papers presented here are all previously unpublished.

This volume marks the 20th anniversary of the New York Number Theory Sem? inar (NYNTS). The seminar began to meet in the Spring, 1982 semester at the CUNY Graduate Center in midtown Manhattan, and has been meeting contin? uously at the Graduate Center for two decades, even as the Graduate Center moved from its original location on 42nd Street near Fifth Avenue to tempo? rary quarters in an office building next to Grand Central Station to a new and elegant building in the former B. Altman department store on Fifth Avenue betwen 34th and 35th Streets. The seminar was originally organized by Harvey Cohn, David and Gregory Chudnovsky, and Melvyn B. Nathanson. In 1982, Harvey Cohn was at City College (CUNY) and the Graduate Center, the Chudnovskys were at Columbia, and Mel Nathanson was at Rutgers. Today, Harvey has retired to California, the Chudnovskys are at Polytechic University of New York, and Nathanson is at Lehman College (CUNY) and the Graduate Center.* The spanning number and the independence number of a subset of an abelian group * A formula related to the Frobenius problem in two dimensions * One bit world * Use of Pad? approximation in spline construction * Interactions between number theory and operator algebras in the study of Riemann zeta function (d'apres Bost-Connes and Connes) * A hyperelliptic curve with real multiplication of degree two * Humbert's conic model and the Kummer surface * Arithmeticity and theta correspondence of an orthogonal group * Morphis heights and periodic pointsl£#