Uniform Distribution of Sequences of Integers in Residue Classes

Cover......Page 1
Uniform Distribution of Sequences of Integers in Residue Classes......Page 2
0387138722......Page 3
Introduction......Page 6
Contents......Page 8
§ 1. Uniform distribution (mod N)......Page 10
§ 2. The sets M(f)......Page 13
§ 3. Weak uniform distribution (mod N)......Page 17
§ 4. Uniform distribution of systems of sequences......Page 18
Exercises......Page 20
§ 1. Permutation polynomials......Page 21
§ 2. Generators for the group of permutation polynomials......Page 23
§ 3. Hermite\'s characterization of permutation polynomials......Page 24
§ 4. Examples......Page 27
§ 5. Consequences of Fried\'s theorem......Page 30
§ 6. Weak uniform distribution (mod N) of polynomials......Page 32
§ 7. Notes and comments......Page 34
Exercises......Page 35
§ 1. Principal properties......Page 37
§ 2. Uniform distribution (mod p) of second-order linear recurrences......Page 41
§ 3. General modulus......Page 47
§ 4. Notes and comments......Page 57
Exercises......Page 59
§ 1. The criterion of Delange......Page 60
§ 2. Application of Delange\'s tauberian theorem......Page 63
§ 3. The sets M(f) for additive functions......Page 67
4. Notes and comments......Page 68
Exercises......Page 69
§ 1. Dirichlet -WUD......Page 71
§ 2. Decent functions......Page 80
§ 3. The number of divisors and Euler φ-function......Page 86
§ 4. The vanishing of the sum (5.2)......Page 88
§ 5. The equality Λ_m(N) = G(N)......Page 94
§ 6. Ramanujan\'s τ-function.......Page 97
§ 7. Notes and comments......Page 103
Exercises......Page 104
§ 1. Generating G(N) by the set of values of a polynomial......Page 105
§ 2. An algorithm......Page 111
§ 3. Applications to the study of M*(f)......Page 113
§ 4. The functions σ_k for k \\geq 3......Page 116
§ 5. Notes and comments......Page 121
Exercises......Page 122
References......Page 123
Index......Page 131
Addenda......Page 134