## Number Theory: A Seminar Held at the Graduate School and University Center of the City University of New York 1985-88David V. Chudnovsky, Gregory V. Chudnovsky, Harvey Cohn, Melvyn B. Nathanson 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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### Contents

BUMP J HOFFSTEIN Some Conjectured Relationships Between | 1 |

Arithmetic of Linear Differential Equations Some Diophantine | 12 |

H COHN Iteration of TwoValued Modular Equations | 59 |

Copyright | |

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abelian additive algebraic Analysis analytic appear Applications approximations arithmetic assume asymptotic basis bases basis of order bound characteristic Chudnovsky closed coefficients cohomology complex computation condition congruences conjecture consider construction contains continued corresponding defined denote determined difference Edited elements elliptic curves estimate exact example exists expansions fact factors field finite fixed formula fraction function given gives hypergeometric implies infinite integers known Lamé equation Lemma linear differential equations Math method modular multiplicative Nathanson Note NS(X Number Theory obtain order h ordinary p-adic parameter period points poles polynomial positive prime problem Proceedings proof properties proved quadratic rational relations representation represented ring roots satisfy sequence singular solutions squares sufficiently supersingular surfaces Theorem theory transform values variety zero