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.