Additive Number Theory of Polynomials over a Finite Field - Rilegato

Effinger, Gove W.; Hayes, David R.

Rilegato

ISBN 10: 019853583X ISBN 13: 9780198535836

Casa editrice: Clarendon Press, 1991

Riassunto

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.

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Recensione

'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

Contenuti

The polynomial Waring and Goldbach problems; Local singular series; Local Gauss sums and local derivatives; The adèle ring over k; L-functions of Dirichlet type; The polynomial 3-primes generating function; The polynomial 3-primes problem: an asymptotic solution; The polynomial Waring problem; Appendix: A complete solution to the 3-primes problem; Bibliography; Index.

Dettagli dell'edizione

• Editore: Clarendon Press
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 019853583X
• ISBN 13: 9780198535836
• Rilegatura: Copertina rigida
• Numero di pagine: 174
• Contatto del produttore: Messaggerie Libri; ufficio.anagrafiche@meli.it; ; Via Verdi, 8.; Assago Milano; 20090; Italia