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

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. Addictive Number Theory -- Sum-product Theorems And Applications -- Can You Hear The Shape Of A Beatty Sequence? -- Variance Of Signals And Their Finite Fourier Transforms -- Sparse Sets In Time And Frequency Related To Diophantine Problems And Integrable Systems -- Addition Theorems In Acyclic Semigroups -- Small Sumsets In Free Products Of Mathbb{z}/2\mathbb{z} -- A Combinatorial Approach To Sums Of Two Squares And Related Problems -- A Note On Elkin’s Improvement Of Behrend’s Construction -- Distinct Matroid Base Weights And Additive Theory -- The Postage Stamp Problem And Essential Subsets In Integer Bases -- A Universal Stein-tomas Restriction Estimate For Measures In Three Dimensions -- On The Exact Order Of Asymptotic Bases And Bases For Finite Cyclic Groups -- The Erd?s–turán Problem In Infinite Groups -- A Tiling Problem And The Frobenius Number -- Sumsets And The Convex Hull -- Explicit Constructions Of Infinite Families Of Mstd Sets -- An Inverse Problem In Number Theory And Geometric Group Theory -- Cassels Bases -- Asymptotics Of Weighted Lattice Point Counts Inside Dilating Polygons -- Support Bases Of Solutions Of A Functional Equation Arising From Multiplication Of Quantum Integers And The Twin Primes Conjecture -- Exponential Sums And Distinct Points On Arcs -- New Vacca-type Rational Series For Euler’s Constant ? And Its “alternating” Analog Ln \frac{4}{\pi } -- Mixed Sums Of Primes And Other Terms -- Classes Of Permutation Polynomials Based On Cyclotomy And An Additive Analogue. David Chudnovsky, Gregory Chudnovsky, Editors. Includes Bibliographical References. 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