This volume develops all the tools needed to provide modern, `adelic' proofs of the polynomial analogs to two of the most famous theorems of classical additive number theory: Vinogradov's 3-Primes Theorem and the Waring Problem.

The polynomial Waring and Goldbach problems; Local singular series; Local Gauss sums and local derivatives; The adele 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.

Gove W. Effinger , Department of Mathematics, Skidmore College, New York, USA, David R. Hayes , Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA

'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 |d 12/07/1994