Additive Number Theory

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

By: David Chudnovsky (Editor), Gregory Chudnovsky (Editor)

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Hardcover | 1 September 2010

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376 Pages

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23.5 x 15.88 x 2.54

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The book, just as the work of Mel Nathanson, to whom the contributions are dedicated, deals with additive number theory. The volume provides the current snapshot of the state of the art in this field. For any reader, even for those starting at the advanced high school level of mathematics, the book provides a broad introduction to the current state of the additive number theory. The field is enjoying quite a renaissance recently, judging by the number of publications and a number of Fields medals awarded to mathematicians in this field. Additive number theory has widely ranging applications in the real world in addition to many purely mathematical applications. Applications include, but are not limited to: communication theory and digital signal processing (like cell phone and other wireless applications), image processing, optimization, discrete geometry, etc.

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Addictive Number Theory	p. 1
Sum-Product Theorems and Applications	p. 9
Can You Hear the Shape of a Beatty Sequence?	p. 39
Variance of Signals and Their Finite Fourier Transforms	p. 53
Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems	p. 77
Addition Theorems in Acyclic Semigroups	p. 99
Small Sumsets in Free Products of Z/2Z	p. 105
A Combinatorial Approach to Sums of Two Squares and Related Problems	p. 115
A Note on Elkin's Improvement of Behrend's Construction	p. 141
Distinct Matroid Base Weights and Additive Theory	p. 145
The Postage Stamp Problem and Essential Subsets in Integer Bases	p. 153
A Universal Stein-Tomas Restriction Estimate for Measures in Three Dimensions	p. 171
On the Exact Order of Asymptotic Bases and Bases for Finite Cyclic Groups	p. 179
The Erdos-Turán Problem in Infinite Groups	p. 195
A Tiling Problem and the Frobenius Number	p. 203
Sumsets and the Convex Hull	p. 221
Explicit Constructions of Infinite Families of MSTD Sets	p. 229
An Inverse Problem in Number Theory and Geometric Group Theory	p. 249
Cassels Bases	p. 259
Asymptotics of Weighted Lattice Point Counts Inside Dilating Polygons	p. 287
Support Bases of Solutions of a Functional Equation Arising From Multiplication of Quantum Integers and the Twin Primes Conjecture	p. 303
Exponential Sums and Distinct Points on Arcs	p. 319
New Vacca-Type Rational Series for Euler's Constant ¿ and Its "Alternating" Analog In 4/¿	p. 331
Mixed Sums of Primes and Other Terms	p. 341
Classes of Permutation Polynomials Based on Cyclotomy and an Additive Analogue	p. 355
Table of Contents provided by Ingram. All Rights Reserved.

Additive Number Theory

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

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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