Additive Number Theory of Polynomials over a Finite Field

Additive Number Theory of Polynomials over a Finite Field



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Additive Number Theory of Polynomials over a Finite Field by Gove W. Effinger, David R. Hayes

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.

Product Details

ISBN-13: 9780198535836
Publisher: Oxford University Press, USA
Publication date: 11/07/1991
Series: Oxford Mathematical Monographs Series
Pages: 176
Product dimensions: 6.44(w) x 9.50(h) x 0.63(d)

About the Author

Skidmore College, New York

University of Massachusetts, Amherst

Table of Contents

1. The Polynomial Waring and Goldbach Problems
2. Local Singular Series
3. Local Gauss Sums and Local Derivatives
4. The Adele Ring over k
5. L-functions of Dirichlet Type
6. The Polynomial 3-Primes Generating Function
7. The Polynomial 3-Primes Problem: An Asymptotic Solution
8. The Polynomial Waring Problem

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