目录 Introduction 1 Gauss Sums 1.1 Elementary properties of Gauss sums over Fq, 1.2 The reciprocity theorem for quadratic Gauss sums, 1.3 Gauss' evaluation of a quadratic Gauss sum, 1.4 Estermann's evaluation of a quadratic Gauss sum, 1.5 Elementary determination of quadratic Gauss sums, 1.6 Gauss character sums over the ring of integers (rood k), Exercises 1, Notes on Chapter 1, 2 Jacobi Sums and Cyclotomic Numbers 2.1 Basic properties of Jacobi sums over F~, 2.2 Cyclotomic numbers, 2.3 Cyclotomic numbers of order 3, 2.4 Cyclotomic numbers of order 4, 2.5 Relationship between Jacobi sums and cyclotomic numbers, 2.6 Determination of indg2 and indgk (mod k), 2.7 Generalized cyclotomic numbers and the determination of ind,/(mod k), Exercises 2, Notes on Chapter 2, 3 Evaluation of Jacobi Sums over Fp 3.1 Cubic and sextic sums, 3.2 Quartic sums, 3.3 Octic sums, 3.4 Bioctic sums, 3.5 Duodecic sums, 3.6 Biduodecic sums, 3.7 Quintic and decic sums, 3.8 Bidecic sums, 3.9 Septic sums, Exercises 3, Notes on Chapter 3, 4 Determination of Gauss Sums over Fp 4.1 The Gauss sumsg(3) andg(6), 4.2 The Gauss sum g(4), 4.3 The Gauss sum g(8), 4.4 The Gauss sum g(12), Exercises 4, Notes on Chapter 4, 5 Difference Sets 5.1 Basic definitions, 5.2 Necessary and sufficient conditions for power residue difference sets, 5.3 Applications of Gauss sums, Exercises 5, Notes on Chapter 5, 6 Jacobsthal Sums over Fp 6.1 Jacobsthal sums and their elementary properties, 6.2 Explicit determination of some Jacobsthal sums, 6.3 Applications to the distribution of quadratic residues
占位居中
直播中，去观看