The Finite Field Distance Problem

David J. Covert (Autor)

Buch | Softcover

181 Seiten

2021
American Mathematical Society (Verlag)
978-1-4704-6031-0 (ISBN)

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Erdos asked how many distinct distances must there be in a set of $n$ points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of a compact set in order to guarantee that the set of distinct distances has positive Lebesgue measure in $R$. The finite field distance problem poses the analogous question in a vector space over a finite field. The problem is relatively new but remains tantalizingly out of reach. This book provides an accessible, exciting summary of known results. The tools used range over combinatorics, number theory, analysis, and algebra. The intended audience is graduate students and advanced undergraduates interested in investigating the unknown dimensions of the problem. Results available until now only in the research literature are clearly explained and beautifully motivated. A concluding chapter opens up connections to related topics in combinatorics and number theory: incidence theory, sum-product phenomena, Waring's problem, and the Kakeya conjecture.

David J. Covert, University of Missouri, St. Louis, MO.

Background
The distance problem
The Iosevich-Rudnev bound
Wolff's exponent
Rings and generalized distances
Configurations and group actions
Combinatorics in finite fields
Bibliography
Index

Erscheinungsdatum	05.05.2021
Reihe/Serie	Carus Mathematical Monographs
Verlagsort	Providence
Sprache	englisch
Maße	140 x 216 mm
Gewicht	245 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4704-6031-9 / 1470460319
ISBN-13	978-1-4704-6031-0 / 9781470460310
Zustand	Neuware