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

1 | |

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 |

### Common terms and phrases

Additive Combinatorics Additive Number Theory algebraic assume asymptotic basis bases basis of order Birthday of Melvyn Chudnovsky and G Chudnovsky eds coefficients Combinatorics Conjecture contains Corollary defined denote discrete Fourier transform e-mail eigenvalue eigenvectors elements Erd˝os estimate exact asymptotic basis exists Festschrift In Honor Fibonacci number finite set fixed point formula Fourier matrix Fourier transform fp(q Freiman’s Functional Equation geometric group theory Hence Hilbert matrix inequality infinite interval ISSN lattice points Lemma linear lower bound M. B. Nathanson Math Mathematics Subject Classifications matroid modulo MSTD sets N-set non-negative integers odd prime order h permutation polynomials Pn-set polygon positive integers Proof of Theorem Proposition prove quantum integers real numbers rectangle relatively prime representation result satisfying Functional Equation semigroup solutions Springer Science+Business Media Subject Classifications 2010 Szeg¨o tiled Uncertainty Principle vector