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.
Author(s): Melvyn B. Nathanson (auth.), David Chudnovsky, Gregory Chudnovsky (eds.)
Edition: 1
Publisher: Springer-Verlag New York
Year: 2010
Language: English
Pages: 361
Tags: Number Theory; Algebra; Mathematical Logic and Foundations
Front Matter....Pages i-xi
Addictive Number Theory....Pages 1-8
Sum-Product Theorems and Applications....Pages 9-38
Can You Hear the Shape of a Beatty Sequence?....Pages 39-52
Variance of Signals and Their Finite Fourier Transforms....Pages 53-76
Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems....Pages 77-98
Addition Theorems in Acyclic Semigroups....Pages 99-104
Small Sumsets in Free Products of $$\mathbb{Z}/2\mathbb{Z}$$ ....Pages 105-113
A Combinatorial Approach to Sums of Two Squares and Related Problems....Pages 115-140
A Note on Elkin’s Improvement of Behrend’s Construction....Pages 141-144
Distinct Matroid Base Weights and Additive Theory....Pages 145-151
The Postage Stamp Problem and Essential Subsets in Integer Bases....Pages 153-169
A Universal Stein-Tomas Restriction Estimate for Measures in Three Dimensions....Pages 171-178
On the Exact Order of Asymptotic Bases and Bases for Finite Cyclic Groups....Pages 179-193
The Erdős–Turán Problem in Infinite Groups....Pages 195-202
A Tiling Problem and the Frobenius Number....Pages 203-220
Sumsets and the Convex Hull....Pages 221-227
Explicit Constructions of Infinite Families of MSTD Sets....Pages 229-248
An Inverse Problem in Number Theory and Geometric Group Theory....Pages 249-258
Cassels Bases....Pages 259-285
Asymptotics of Weighted Lattice Point Counts Inside Dilating Polygons....Pages 287-301
Support Bases of Solutions of a Functional Equation Arising From Multiplication of Quantum Integers and the Twin Primes Conjecture....Pages 303-317
Exponential Sums and Distinct Points on Arcs....Pages 319-330
New Vacca-Type Rational Series for Euler’s Constant γ and Its “Alternating” Analog $$\ln \frac{4}{\pi }$$ ....Pages 331-340
Mixed Sums of Primes and Other Terms....Pages 341-353
Classes of Permutation Polynomials Based on Cyclotomy and an Additive Analogue....Pages 355-361
