Number Theory and Number Crunching

Kapitel in diesem Buch

1. Frontmatter I
2. CONTENTS V
3. FOREWORD IX
4. PREFACE XI
5. I. DIOPHANTINE APPROXIMATIONS AND TRANSCENDENTAL NUMBER THEORY
6. Polynomials of Minimal Diophantic Relative Deviation from Zero on the Interval [0,1] 3
7. A Theorem of Gelfond via Schneider's Method 9
8. An Estimation of the Difference Between Two Zeros of a Polynomial 17
9. On the Arithmetic Properties of the Values of E-Functions 23
10. Approximation of Irrationals by m/n, Satisfying f (m/n)=a 31
11. II. FORMS AND CONGRUENCES
12. Discriminants of Decomposable Forms 39
13. On Some Entire Modular Forms of Half Integral Weight on the Group г_o(4N) 57
14. On Solutions of Linear Congruences 69
15. III. METRIC NUMBER THEORY
16. The Method of Trigonometric Sums and Lower Estimates of Hausdorff Dimension 75
17. The Optimal Zone for Large Deviations of the Denominators of Continued Fractions 83
18. Ergodic Properties of Multi-Dimensional Subtractive Algorithms 91
19. IV. MULTIPLICATIVE NUMBER THEORY
20. Selberg's Inequality in Arithmetic Progressions 103
21. Smoothing and Inversion Inequalities 111
22. The Mean Values of Multiplicative Functions Defined on a Semigroup 121
23. Semigroup Elements Free of Large Prime Factors 135
24. On Multiplicative Functions with Regularity Properties 155
25. On an Analytic Problem Considered by Sierpiriski and Ramanujan 165
26. Distribution of Prime Vectors in Integral Lattices 173
27. Multiplicative Functions of Special Type in Short Intervals 181
28. V. DISTRIBUTION OF ADDITIVE FUNCTIONS
29. Smoothness of the Distributions of Arithmetic Functions 191
30. On the Erdos-Wintner Theorem in Banach Spaces 201
31. Additive Arithmetic Functions and Processes with Independent Increments 211
32. On the Modulus of Continuity of the Distribution of Some Arithmetical Functions 223
33. Topics on Arithmetic Functions with Rational Arguments 235
34. Measure Theory and Arithmetical Functions 251
35. Generalizations of Kubilius' Class of Additive Functions. I 269
36. The Multi-Dimensional Local Theorem for Additive Arithmetic Functions 285
37. The von Mises Theorem in Number Theory 293
38. The Law of Large Numbers in the Case of Shifted Primes 311
39. VI. ZETA-FUNCTIONS AND ALGEBRAIC NUMBER THEORY
40. On Some Formulae in Analytic Number Theory. II 319
41. The Atkinson Formula Near the Critical Line 335
42. Large Value Estimates for Hecke Polynomials 355
43. VII. COMPUTATIONAL NUMBER THEORY AND APPLICATIONS TO NUMERIC ANALYSIS
44. On Normal Bases of Algebraic Number Fields 369
45. Number Theory and Number Crunching 379
46. List of Contributors 387