On irregularities of distribution in shifts and dilations of integer sequences, II

Chapters in this book

1. i-iv i
2. Preface v
3. List of participants vii
4. Table of contents of Volume I xi
5. Table of contents of Volume II xv
6. Quelques nouveaux résultats sur les nombres de Pisot et de Salem 1
7. Irreducibility of polynomials and arithmetic progressions with equal products of terms 11
8. Mahler’s measure and special values of L-functions — some conjectures 27
9. On the distribution of solutions of Thue’s equation 35
10. Linear independence and divided derivatives of a Drinfeld module. I 47
11. Cubic threefolds with six double points 63
12. Arithmétique et espaces de modules de revêtements 75
13. On a polynomial with large number of irreducible factors 103
14. Fractions continues paramétrées et critère de Rabinowitsch 111
15. The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group 121
16. On the factorization of polynomials with small Euclidean norm 143
17. Small Salem numbers 165
18. Variables separated polynomials, the genus 0 problem and moduli spaces 169
19. Some polynomial identities related to the abc-conjecture 229
20. On the distribution of solutions of decomposable form equations 237
21. Finding small degree factors of lacunary polynomials 267
22. On the factorization of lacunary polynomials 277
23. Specializations of some hyperelliptic Jacobians 293
24. Salem numbers and Pisot numbers from stars 309
25. On lacunary formal power series and their continued fraction expansion 321
26. The ultra-divergent series Σ_n>̲0 0^-2n 327
27. Une remarque sur l’équation de Catalan 337
28. The work of Andrzej Schinzel in number theory 341
29. Algebraic curves with many rational points over finite fields of characteristic 2 359
30. Arf equivalence I 381
31. The number of irreducible factors of a polynomial, III 395
32. Identities with covering systems and Appell polynomials 407
33. Binary recurring sequences and powers, I 419
34. On Mahler’s measure for polynomials in several variables 431
35. Polynomials that divide many k-nomials 445
36. Solution trees of polynomial congruences modulo prime powers 451
37. The equation a^xn-1_x-1 =by^q with ab>1 473
38. Transcendence bases of the algebra of vector invariants for a symmetric group 487
39. Some applications of Schinzel’s Hypothesis to Diophantine equations 503
40. On the Milnor exact sequence for rational quadratic forms 531
41. Some notes on monodromy groups of polynomials 539
42. Integer valued entire functions on Cartesian products 553
43. On a conjecture of Schinzel and Tijdeman 577
44. List of contributors 583
45. On some convex lattice polytopes 591
46. Digital blocks in linear numeration systems 607
47. On irregularities of distribution in shifts and dilations of integer sequences, II 633
48. Addition of integer sequences and subsets of real tori 639
49. Kloosterman sums for the modular group 651
50. Hecke series values of holomorphic cusp forms in the centre of the critical strip 675
51. Bounds for frequencies of residues of regular second-order recurrences modulo p^r 691
52. Differential inequalities for Iwaniec’s q functions 721
53. When is the product of two Hecke eigenforms an eigenform? 737
54. Grandes valeurs de la fonction d_k 743
55. On a multiplicative analogue of Goldbach’s conjecture 771
56. On two conjectures of Sierpiński concerning the arithmetic functions σ and φ 795
57. Residue classes free of values of Euler’s function 805
58. Gauss’ congruence from Dirichlet’s class number formula and generalizations 813
59. Note on a variance in the distribution of primes 841
60. The distribution of modular symbols 849
61. On the solutions to φ(n) = φ(n + k) 867
62. Lattice points in the sphere 883
63. On the Barban-Davenport-Halberstam theorem: XII 893
64. The integer points close to a curve III 911
65. Dirichlet L-functions at the central point 941
66. The Selberg class: a survey 953
67. A radically simplified Selberg zeta function for the modular group 993
68. The Goldbach-Vinogradov Theorem 1005
69. Α Tauber theorem and multiplicative functions on permutations 1025
70. Extreme values of Dirichlet L-functions at 1 1039
71. On the remainder term in the Selberg sieve 1053
72. Newforms for the modular group on spaces of dimension 2 1065
73. Computational sieving applied to some classical number-theoretic problems 1071
74. Evaluation of mean-values of products of shifted arithmetical functions, II 1081
75. Crible d’Ératosthène et modèle de Kubilius 1099
76. Three two-dimensional Weyl steps in the circle problem, III. Exponential integrals and application 1131
77. From quadratic functions to modular functions 1147
78. List of contributors 1179