Characterizations of the Logarithm as an Additive Arithmetic Function

Chapters in this book

1. Frontmatter I
2. Preface V
3. List of Participants VI
4. Table of Contents XI
5. An Integral Functional Equation of Ramanujan Related to the Dilogarithm 1
6. Cyclotomic Partitions 7
7. Limit Points of the Salem Numbers 27
8. Complexity of Algorithms in Algebraic Number Theory 37
9. Perturbations and Complementary Sequences of Integers 55
10. On the Number of Sets of Integers With Various Properties 61
11. On the Ramanujan-Nagell Equation and its Generalizations 81
12. The Uniform Group Under Change of Rings 93
13. Sieve Auxiliary Functions 99
14. Discriminants and Class Numbers of Indefinite Integral Quadratic Forms 115
15. On a Conjecture of Roth and Some Related Problems, II 125
16. Some New Identities Involving the Partition Function p(n ) 139
17. What is Special about 195? Groups, n th Power Maps and a Problem of Graham 147
18. Modular Elliptic Curves and Diophantine Problems 157
19. Some Conjectures Related to Fermat's Last Theorem 177
20. Canadian Number Theory Association Unsolved Problems 1988 193
21. The Partial Zeta Functions of a Real Quadratic Number Field Evaluated at s = 0 207
22. Characterizations of the Logarithm as an Additive Arithmetic Function 227
23. A Note on Dedekind Sums 239
24. A Brief Survey on Distribution Questions for Second Order Linear Recurrences 249
25. Basis for the Polynomial Time Computable Functions 255
26. Exponential Sums Connected With Quadratic Forms 271
27. On Quartic Fields with the Symmetric Group 287
28. Sets With Non-Squarefree Sums 299
29. Class Numbers of Simplest Quartic Fields 313
30. On Improving Ramachandra’s Unit Index 325
31. Rational Functions, Diagonals, Automata and Arithmetic 339
32. Discriminants and Permutation Groups 359
33. The Riemann Hypothesis From a Logician’s Point of View 387
34. Triangular Farey Arrays 401
35. Solution of the Class Number One Problem For Real Quadratic Fields of Extended Richaud-Degert Type (With One Possible Exception) 417
36. On Simple Zeros of Certain L-Series 427
37. Asymptotic Distribution and Independence of Sequences of g -Adic Integers, II 441
38. On the Piltz Divisor Problem With Congruence Conditions 455
39. On the Pair Correlation of Zeros of Dirichlet L-Functions 471
40. Computational Methods For the Resolution of Diophantine Equations 477
41. Some Confirming Instances of the Birch-Swinnerton-Dyer Conjecture Over Biquadratic Fields 493
42. Criteria for the Class Number of Real Quadratic Fields to be One 501
43. An Analog of Hilbert's Irreducibility Theorem 509
44. On Partitions of the Positive Integers With No x, y, z Belonging to Distinct Classes Satisfying x + y = z 515
45. Algebraic surfaces derived from unit groups of quaternion algebras 529
46. Explicit evaluation of certain Eisenstein sums 553
47. Digital Sum Sets 627
48. New Invariants of Real Quadratic Fields 635
49. A Limit Formula for the Canonical Height of an Elliptic Curve and its Application to Height Computations 641
50. Backmatter 660