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David Chudnovsky, Gregory Chudnovsky, "Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson"

Celebrates the contributions which Melvyn B. Nathanson has made to additive number theory

Provides a current view of the state-of-the-art in the field of additive number theory

Includes contributions to various areas of number theory by top researchers in the field

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.

Contents

.-Preface.- Sum-product theorems and applications (Bourgain).-Can you hear the shape of a Beatty sequence? (Graham, O’Bryant).-Variance of signals and their finite Fourier transforms (Chudnovsky, Chudnovsky, Morgan).-Sparse sets in time and frequency related to diophantine problems and integrable systems (Chudnovsky, Chudnovsky, Morgan).-Addition theorems in acyclic semigroups (Cilleruelo, Hamidoune, Serra).-Small sumsets in free products of Z/2Z (Eliahou, Lecouvey).-A combinatorial approach to sums of two squares and related problems (Elsholtz).-A note on Elkin’s improvement of Behrend’s construction (Green, Wolf).-The postage stamp problem and essential subsets in integer bases (Hegarty).-A universal Stein-Tomas restriction estimate for measures in three dimensions (Iosevich, Roudenko).-The Erdos-Turán problem in infinite groups (Konyagin, Lev).-A tiling problem and the Frobenius number (Labrousse, Ramírez Alfonsín).- Sumsets and the convex hull (Matolcsi, Ruzsa).- Explicit constructions of infinite families of MSTD sets (Miller, Scheinerman).-Asymptotics of weighted lattice point counts inside dilating polygons (Nechayeva, Randol).- Support bases of solutions of a functional equation arising from multiplication of quantum integers and the twin primes conjecture (Nguyen).- Exponential sums and distinct points on arcs (Rødseth).- New Vacca-type rational series for Euler’s constant g and its "alternating" analog ln 4/p (Sondow).- Mixed sums of primes and other terms (Sun).- Classes of permutation polynomials based on cyclotomy and an additive analogue (Zieve).

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