Additive Number Theory of Polynomials Over a Finite Field (Oxford Mathematical Monographs) - Hardcover

Effinger, Gove W.; Hayes, David R.

Hardcover

ISBN 10: 019853583X ISBN 13: 9780198535836

Publisher: Clarendon Press, 1991

Synopsis

This volume is a systematic treatment of the additive number theory of polynomials over a finite field, an area possessing deep and fascinating parallels with classical number theory. In providing asymptomatic proofs of both the Polynomial Three Primes Problem (an analog of Vinogradov's theorem) and the Polynomial Waring Problem, the book develops the various tools necessary to apply an adelic "circle method" to a wide variety of additive problems in both the polynomial and classical settings. A key to the methods employed here is that the generalized Riemann hypothesis is valid in this polynomial setting. The authors presuppose a familiarity with algebra and number theory as might be gained from the first two years of graduate course, but otherwise the book is self-contained. Starting with analysis on local fields, the main technical results are all proved in detail so that there are extensive discussions of the theory of characters in a non-Archimidean field, adele class groups, the global singular series and Radon-Nikodyn derivatives, L-functions of Dirichlet type, and K-ideles.

About this title

Review

'To sum up, the book is an outstanding motivation for and introduction to the study of analytical methods in arithmetic.' mededelingen van het wiskundig genootschap, no.8, - november 1993

Edition details

• Publisher: Clarendon Press
• Publication date: 1991
• Language: English
• ISBN 10: 019853583X
• ISBN 13: 9780198535836
• Binding: Hardcover
• Edition number: 1
• Number of pages: 174