The New York Number Theory Seminar was organized in 1982 to provide a forum for the presentation and discussion of recent advances in higher arithmetic and its applications. Papers included in this volume are based on the lectures presented by their authors at the Seminar at the Graduate Center of C.U.N.Y. in 1985-88. Papers in the volume cover a wide spectrum of number theoretic topics ranging from additive number theory and diophantine approximations to algebraic number theory and relations with algebraic geometry and topology.

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Some conjectured relationships between theta functions and eisenstein series on the metaplectic group.- Computational problems in arithmetic of linear differential equations. Some diophantine applications.- Iteration of two-valued modular equations.- Report on transcendency in the theory of function fields.- Exponential sums and faster than Nyquist signaling.- Some new applications of the large sieve.- Elliptic fiberings of Kummer surfaces.- Recent developments in the theory of rational period functions.- Additive problems in combinatorial number theory.- Growth of order of homology of cyclic branched covers of knots.- Hybrid problems in number theory.- Binomial coefficients not divisible by a prime.- Positive characteristic calculus and icebergs.- Arithmetic of certain algebraic surfaces over finite fields.