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Additive Number Theory

Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson

  • Book
  • © 2010

Overview

Editors:
  1. David Chudnovsky

    1. New York University, Department of Mathematics, Polytechnic Institute of, Brooklyn, USA

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  2. Gregory Chudnovsky

    1. New York University, Department of Mathematics, Polytechnic Institute of, Brooklyn, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Celebrates the contributions which Melvyn B. Nathanson has made to additive number theory

  • This book provides a current look at the state-of-the-art in the field of additive number theory

  • Volume contains contributions to various areas of number theory by top researchers in the field

  • Includes supplementary material: sn.pub/extras

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xi
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  2. Addictive Number Theory

    • Melvyn B. Nathanson
    Pages 1-8

  3. Sum-Product Theorems and Applications

    • Jean Bourgain
    Pages 9-38

  4. Can You Hear the Shape of a Beatty Sequence?

    • Ron Graham, Kevin O’Bryant
    Pages 39-52

  5. Variance of Signals and Their Finite Fourier Transforms

    • D. V. Chudnovsky, G. V. Chudnovsky, T. Morgan
    Pages 53-76

  6. Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems

    • D. V. Chudnovsky, G. V. Chudnovsky, T. Morgan
    Pages 77-98

  7. Addition Theorems in Acyclic Semigroups

    • Javier Cilleruelo, Yahya O. Hamidoune, Oriol Serra
    Pages 99-104

  8. Small Sumsets in Free Products of \(\mathbb{Z}/2\mathbb{Z}\)

    • Shalom Eliahou, Cédric Lecouvey
    Pages 105-113

  9. A Combinatorial Approach to Sums of Two Squares and Related Problems

    • Christian Elsholtz
    Pages 115-140

  10. A Note on Elkin’s Improvement of Behrend’s Construction

    • Ben Green, Julia Wolf
    Pages 141-144

  11. Distinct Matroid Base Weights and Additive Theory

    • Y. O. Hamidoune, I. P. da Silva
    Pages 145-151

  12. The Postage Stamp Problem and Essential Subsets in Integer Bases

    • Peter Hegarty
    Pages 153-169

  13. A Universal Stein-Tomas Restriction Estimate for Measures in Three Dimensions

    • Alex Iosevich, Svetlana Roudenko
    Pages 171-178

  14. On the Exact Order of Asymptotic Bases and Bases for Finite Cyclic Groups

    • Xingde Jia
    Pages 179-193

  15. The Erdős–Turán Problem in Infinite Groups

    • Sergei V. Konyagin, Vsevolod F. Lev
    Pages 195-202

  16. A Tiling Problem and the Frobenius Number

    • D. Labrousse, J. L. Ramírez Alfonsín
    Pages 203-220

  17. Sumsets and the Convex Hull

    • Máté Matolcsi, Imre Z. Ruzsa
    Pages 221-227

  18. Explicit Constructions of Infinite Families of MSTD Sets

    • Steven J. Miller, Daniel Scheinerman
    Pages 229-248

  19. An Inverse Problem in Number Theory and Geometric Group Theory

    • Melvyn B. Nathanson
    Pages 249-258

  20. Cassels Bases

    • Melvyn B. Nathanson
    Pages 259-285
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Keywords

About this book

This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. Nathanson's numerous results have been widely published in top notch journals and in a number of excellent graduate textbooks (GTM Springer) and reference works. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.

Editors and Affiliations

  • New York University, Department of Mathematics, Polytechnic Institute of, Brooklyn, USA

    David Chudnovsky, Gregory Chudnovsky

Bibliographic Information

  • Book Title: Additive Number Theory

  • Book Subtitle: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson

  • Editors: David Chudnovsky, Gregory Chudnovsky

  • DOI: https://doi.org/10.1007/978-0-387-68361-4

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2010

  • Hardcover ISBN: 978-0-387-37029-3Published: 01 September 2010

  • Softcover ISBN: 978-1-4899-8146-2Published: 03 September 2014

  • eBook ISBN: 978-0-387-68361-4Published: 26 August 2010

  • Edition Number: 1

  • Number of Pages: XI, 361

  • Topics: Number Theory, Algebra, Mathematical Logic and Foundations

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