Additive Number Theory of Polynomials over a Finite Field

Gove W. Effinger, David R. Hayes

ISBN 10: 019853583X / ISBN 13: 9780198535836

Published by Oxford University Press, GB, 1991

About this Item

This volume is a systematic treatment of the additive number theory of polynomials over a finite field, an area possessing fascinating and deep parallels with classical number theory. In providing asymptotic 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 Generalised 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 a graduate course, but otherwise the book is self-contained.

Seller Inventory # LU-9780198535836

Bibliographic Details

• Title: Additive Number Theory of Polynomials over a Finite Field
• Publisher: Oxford University Press, GB
• Publication Date: 1991
• Language: English
• ISBN 10: 019853583X
• ISBN 13: 9780198535836
• Binding: Hardback
• Condition: New
• Weight: 416 grams

About this title

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.

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