Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson

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