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The Finite Field Distance Problem Carus Mathematical Monographs David J Covert Author

SKU: BELL-51992380

$ 31.00 ~~$ 45.00~~ (-31%)

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The Finite Field Distance Problem Carus Mathematical Monographs David J Covert Author instant download after payment.

Publisher: American Mathematical Society

File Extension: PDF

File size: 3.12 MB

Pages: 181

Author: David J. Covert (author)

ISBN: 9781470460310, 1470460319

Language: English

Year: 2021

Volume: 37

Product desciption

The Finite Field Distance Problem Carus Mathematical Monographs David J Covert Author by David J. Covert (author) 9781470460310, 1470460319 instant download after payment.

Erdős 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.