Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson (Google eBook)

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Springer Science & Business Media, Aug 26, 2010 - Mathematics - 372 pages
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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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Contents

Addictive Number Theory
1
SumProduct Theorems and Applications
9
Can You Hear the Shape of a Beatty Sequence?
39
Variance of Signals and Their Finite Fourier Transforms
53
Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems
77
Addition Theorems in Acyclic Semigroups
99
Small Sumsets in Free Products of z2z
105
A Combinatorial Approach to Sums of Two Squares and Related Problems
115
The ErdosTurán Problem in Infinite Groups
194
A Tiling Problem and the Frobenius Number
203
Sumsets and the Convex Hull
221
Explicit Constructions of Infinite Families of MSTD Sets
229
An Inverse Problem in Number Theory and Geometric Group Theory
249
Cassels Bases
259
Asymptotics of Weighted Lattice Point Counts Inside Dilating Polygons
286
Support Bases of Solutions of a Functional Equation Arising From Multiplication of Quantum Integers and the Twin Primes Conjecture
303

A Note on Elkins Improvement of Behrends Construction
141
Distinct Matroid Base Weights and Additive Theory
145
The Postage Stamp Problem and Essential Subsets in Integer Bases
152
A Universal SteinTomas Restriction Estimate for Measures in Three Dimensions
171
On the Exact Order of Asymptotic Bases and Bases for Finite Cyclic Groups
179
Exponential Sums and Distinct Points on Arcs
318
New VaccaType Rational Series for Eulers Constant and Its Alternating Analog ln4
331
Mixed Sums of Primes and Other Terms
341
Classes of Permutation Polynomials Based on Cyclotomy and an Additive Analogue
355
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