Gauss and Jacobi Sums

Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today′s sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy.

Spis treści:
Gauss Sums.
Jacobi Sums and Cyclotomic Numbers.
Evaluation of Jacobi Sums Over Fp.
Determination of Gauss Sums Over Fp.
Difference Sets.
Jacobsthal Sums Over Fp.
Residuacity.
Reciprocity Laws.
Congruences for Binomial Coefficients.
Diagonal Equations over Finite Fields.
Gauss Sums over Fq.
Eisenstein Sums.
Brewer Sums.
A General Eisenstein Reciprocity Law.
Research Problems.
Bibliography.
Notation.
Indexes.