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Number Theory

New York Seminar 1991–1995

  • Book
  • © 1996

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Editors:
  1. David V. Chudnovsky

    1. Department of Mathematics, Columbia University, New York, USA

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  2. Gregory V. Chudnovsky

    1. Department of Mathematics, Columbia University, New York, USA

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  3. Melvyn B. Nathanson

    1. Department of Mathematics Lehman College, City University of New York, Bronx, USA

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Sums of Four Squares

    • Richard T. Bumby
    Pages 1-8

  3. On the Number of Co-Prime-Free Sets

    • Neil J. Calkin, Andrew Granville
    Pages 9-18

  4. The Primary Role of Modular Equations

    • Harvey Cohn
    Pages 19-41

  5. Approximation Methods in Transcendental Function Computations and Some Physical Applications

    • D. V. Chudnovsky, G. V. Chudnovsky
    Pages 43-69

  6. Diophantine Approximation Problem Arising from VLSI Design

    • D. V. Chudnovsky, G. V. Chudnovsky
    Pages 71-90

  7. Linear Diophantine Problems

    • Mehdi Djawadi, Gerd Hofmeister
    Pages 91-95

  8. On the Sum of the Reciprocals of the Differences Between Consecutive Primes

    • Paul Erdös, Melvyn B. Nathanson
    Pages 97-101

  9. The Smallest Maximal Set of Pairwise Disjoint Partitions

    • Michael Filaseta
    Pages 103-113

  10. Sum Set Cardinalities of Line Restricted Planar Sets

    • Peter C. Fishburn
    Pages 115-133

  11. On Solvability of a System of Two Boolean Linear Equations

    • Gregory Freiman
    Pages 135-150

  12. “Brauer Numbers” of Twisted Fermat Motives

    • Fernando Q. Gouvea, Noriko Yui
    Pages 151-175

  13. A Remark on a Paper of Erdős and Nathanson

    • R. L. Graham
    Pages 177-179

  14. Towards a Classification of Hilbert Modular Threefolds

    • H. G. Grundman
    Pages 181-193

  15. Special Theta Relations

    • William F. Hammond
    Pages 195-199

  16. Minimal Bases and g-Adic Representations of Integers

    • Xing-De Jia
    Pages 201-209

  17. Finite Graphs and the Number of Sums and Products

    • Xing-De Jia, Melvyn B. Nathanson
    Pages 211-219

  18. Hilberth’s Theorem 94 and Function Fields

    • Howard Kleiman
    Pages 221-228

  19. Some Applications of Probability to Additive Number Theory and Harmonic Analysis

    • Mihail N. Kolountzakis
    Pages 229-251

  20. Quadratic Irrationals and Continued Fractions

    • Joseph Lewittes
    Pages 253-268
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About this book

This volume is dedicated to Harvey Cohn, Distinguished Professor Emeritus of Mathematics at City College (CUNY). Harvey was one of the organizers of the New York Number Theory Seminar, and was deeply involved in all aspects of the Seminar from its first meeting in January, 1982, until his retirement in December, 1995. We wish him good health and continued hapiness and success in mathematics. The papers in this volume are revised and expanded versions of lectures delivered in the New York Number Theory Seminar. The Seminar meets weekly at the Graduate School and University Center of the City University of New York (CUNY). In addition, some of the papers in this book were presented at a conference on Combinatorial Number Theory that the New York Number Theory Seminar organized at Lehman College (CUNY). Here is a short description of the papers in this volume. The paper of R. T. Bumby focuses on "elementary" fast algorithms in sums of two and four squares. The actual talk had been accompanied by dazzling computer demonstrations. The detailed review of H. Cohn describes the construction of modular equations as the basis of studies of modular forms in the one-dimensional and Hilbert cases.

Editors and Affiliations

  • Department of Mathematics, Columbia University, New York, USA

    David V. Chudnovsky, Gregory V. Chudnovsky

  • Department of Mathematics Lehman College, City University of New York, Bronx, USA

    Melvyn B. Nathanson

Bibliographic Information

  • Book Title: Number Theory

  • Book Subtitle: New York Seminar 1991–1995

  • Editors: David V. Chudnovsky, Gregory V. Chudnovsky, Melvyn B. Nathanson

  • DOI: https://doi.org/10.1007/978-1-4612-2418-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1996

  • Softcover ISBN: 978-0-387-94826-3Published: 19 September 1996

  • eBook ISBN: 978-1-4612-2418-1Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 297

  • Number of Illustrations: 12 b/w illustrations

  • Topics: Number Theory

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