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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.
Sommario
Preface.- 1 The Spanning Number and the Independence Number of a Subset ofan Abelian Group.- 2 A Formula Related to the Frobenius Problem in Two Dimensions.- 3 One Bit World.- 4 Use of Padé Approximation in Spline Construction.- 5 Interactions between Number Theory and Operator Algebras in the Study ofthe Riemann Zeta Function (d'aprés Bost-Connes and Connes).- 6 A Hyperelliptic Curve with Real Multiplication of Degree Two.- 7 Humbert's Conic Model and the Kummer Surface.- 8 Arithmeticity and Theta Correspondence of an Orthogonal Group.- 9 Morphic Heights and Periodic Points.- 10 The Elementary Proofofthe Prime Number Theorem: An Historical Perspective.- 11 Additive Bases Representations and the Erd?s-Turán Conjecture.- 12 The Boundary Structure ofthe Sumset in Z2.- 13 On NTUs in Function Fields.- 14 Continued Fractions and Quadratic Irrationals.- 15 The Inverse Problem for Representation Functions of Additive Bases.- 16 On the Uniquity of Sidon Sets.
