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

by David Chudnovsky (Editor), Gregory Chudnovsky (Editor)

Overview

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.

Product Details

ISBN-13:	9780387370293
Publisher:	Springer New York
Publication date:	09/01/2010
Edition description:	2010
Pages:	361
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Addictive Number Theory Melvyn B. Nathanson 1

Sum-Product Theorems and Applications Jean Bourgain 9

Can You Hear the Shape of a Beatty Sequence? Ron Graham Kevin O'Bryant 39

Variance of Signals and Their Finite Fourier Transforms D.V. Chudnovsky G.V. Chudnovsky T. Morgan 53

Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems D.V. Chudnovsky G.V. Chudnovsky T. Morgan 77

Addition Theorems in Acyclic Semigroups Javier Cilleruelo Yahya O. Hamidoune Oriol Serra 99

Small Sumsets in Free Products of Z/2Z Shalom Eliahou Cédric Lecouvey 105

A Combinatorial Approach to Sums of Two Squares and Related Problems Christian Elsholtz 115

A Note on Elkin's Improvement of Behrend's Construction Ben Green Julia Wolf 141

Distinct Matroid Base Weights and Additive Theory Y.O. Hamidoune I.P. da Silva 145

The Postage Stamp Problem and Essential Subsets in Integer Bases Peter Hegarty 153

A Universal Stein-Tomas Restriction Estimate for Measures in Three Dimensions Alex Iosevich Svetlana Roudenko 171

On the Exact Order of Asymptotic Bases and Bases for Finite Cyclic Groups Xingde Jia 179

The Erdos-Turán Problem in Infinite Groups Sergei V. Konyagin Vsevolod F. Lev 195

A Tiling Problem and the Frobenius Number D. Labrousse J.L. Ramírez Alfonsín 203

Sumsets and the Convex Hull Máté Matolcsi Imre Z. Ruzsa 221

Explicit Constructions of Infinite Families of MSTD Sets Steven J. Miller Daniel Scheinerman 229

An Inverse Problem in Number Theory and Geometric Group Theory Melvyn B. Nathanson 249

Cassels Bases Melvyn B. Nathanson 259

Asymptotics of Weighted Lattice Point Counts Inside Dilating Polygons Marina Nechayeva Burton Randol 287

Support Bases of Solutions of a Functional Equation Arising From Multiplication of Quantum Integers and the Twin Primes Conjecture Lan Nguyen 303

Exponential Sums and Distinct Points on Arcs Øystein J. Rødseth 319

New Vacca-Type Rational Series for Euler's Constant γ and Its "Alternating" Analog In 4/π Jonathan Sondow 331

Mixed Sums of Primes and Other Terms Zhi-Wei Sun 341

Classes of Permutation Polynomials Based on Cyclotomy and an Additive Analogue Michael E. Zieve 355