CONVOLUTIONS OF THE POISSON LAWS IN NUMBER THEORY

Chapters in this book

1. i-iv i
2. CONTENTS v
3. PREFACE viii
4. Part One. ALGEBRAIC NUMBER THEORY
5. GEL’FOND’S TRANSCENDENCE METHOD BY ELEMENTARY MEANS 3
6. ALGEBRAIC CONJUGATES OUTSIDE THE UNIT CIRCLE 11
7. APPLICATIONS OF ALGEBRAIC UNITS 23
8. ON SOME DIOPHANTINE EQUATIONS CONNECTED WITH PELLIAN EQUATION 27
9. Part Two. QUADRATIC FORMS
10. ON THE GENERAL UNIMPROVABLE ESTIMATES OF THE SINGULAR SERIES OF POSITIVE QUADRATIC FORMS 35
11. ON THE REPRESENTATION OF NUMBERS BY CERTAIN QUADRATIC FORMS IN TEN VARIABLES 45
12. Part Three. ZETA AND L-FUNCTIONS
13. THE UNIVERSALITY THEOREM WITH WEIGHT FOR THE LERCH ZETA-FUNCTION 59
14. THE GENERAL ADDITIVE DIVISOR PROBLEM AND MOMENTS OF THE ZETA-FUNCTION 69
15. THE CORRESPONDENCE BETWEEN A DIRICHLET SERIES AND ITS COEFFICIENTS 91
16. A NOTE ON THE MEAN SQUARE OF Ϛ(s) IN THE CRITICAL STRIP 107
17. EXPLICIT FORMULAS AND ASYMPTOTIC EXPANSIONS FOR CERTAIN MEAN SQUARE OF HURWITZ ZETA-FUNCTIONS. II 119
18. ON LIMIT DISTRIBUTION OF THE LERCH ZETA-FUNCTION 135
19. THE FOURTH MOMENTS OF DIRICHLET SERIES 149
20. Part Four. MULTIPLICATIVE NUMBER THEORY
21. ESTIMATION OF A CERTAIN FUNCTION RELATED TO THE DIRICHLET DIVISOR PROBLEM 171
22. ON SOME PAIRS OF MULTIPLICATIVE FUNCTIONS CORRELATED BY AN EQUATION 191
23. A CHARACTERIZATION OF SOME ADDITIVE ARITHMETICAL FUNCTIONS 205
24. ON PSEUDOSQUARES 213
25. A REMARK ON SOME SPECIAL ARITHMETICAL FUNCTIONS 221
26. MODIFIED ZETA FUNCTIONS AND THE NUMBER OF g-INTEGERS 247
27. Part Five. VALUE DISTRIBUTION OF ARITHMETIC FUNCTIONS
28. ON A CONJECTURE BY ERDÖS AND ITS EXTENSION TO ADDITIVE FUNCTIONS ON THE SET OF PAIRS OF INTEGERS 261
29. MULTIPLICATIVE FUNCTIONS AND STOCHASTIC PROCESSES 271
30. CONVOLUTIONS OF THE POISSON LAWS IN NUMBER THEORY 283
31. SHIFTED PRIMES AND KUBILIUS MODELS 297
32. THE DISTRIBUTION OF THE NUMBER OF PRIME DIVISORS OF NUMBERS OF FORM ab + 1 313
33. MULTIPLICATIVE FUNCTIONS OF FAREY FRACTIONS 323
34. ON SOME INEQUALITIES IN THE PROBABILISTIC NUMBER THEORY 345
35. THE ASYMPTOTICAL EXPANSION IN THE MEAN VALUE THEOREM FOR MULTIPLICATIVE FUNCTIONS 357
36. LOCAL DISTRIBUTIONS OF ARITHMETIC FUNCTIONS ON SEMIGROUPS 363
37. THE MEAN VALUES OF MULTIPLICATIVE FUNCTIONS. III 371
38. ON THE CONVERGENCE TO THE POISSON LAW 389
39. Part Six. PROBABILISTIC THEORY OF NUMBER SYSTEMS AND SERIES
40. RENORMALIZATION OF ALGORITHMS IN THE PROBABILISTIC SENSE 401
41. PROBABILISTIC THEORY OF ADDITIVE FUNCTIONS RELATED TO SYSTEMS OF NUMERATION 413
42. ON LIMIT THEOREMS FOR ENDOMORPHISMS OF A. RÉNYI TYPE 431
43. DENSITIES FOR SUMS OF INDEPENDENT RANDOM VARIABLES AND THEIR APPLICATIONS TO THE VALUE DISTRIBUTIONS OF Δ(x), P(x) AND ς(s) 441
44. Part Seven. MISCELLANEOUS
45. NOTE ON THE TRANSCENDENCE OF A GENERATING FUNCTION 461
46. SOLUTION OF THE EQUATIONS OF DYNAMICAL CHAOS 467
47. LOGISTIC DIFFERENTIAL EQUATION OF NEUTRAL TYPE 475
48. A THEOREM OF MÜNTZ TYPE FOR CHEBYSHEV POLYNOMIALS 485
49. COMPLETE SYSTEMS OF HOLOMORPHIC FUNCTIONS 489
50. Programme of the Conference 500