Paul Turán and Probabilistic Number Theory

Chapters in this book

1. Frontmatter i
2. Preface v
3. List of contributing authors vii
4. Contents xi
5. Random union-closed families 1
6. Small populations of zeros of L-functions 11
7. Turán-type inequalities and the distribution of zeros of entire functions 25
8. Paul Turán and Probabilistic Number Theory 41
9. Effective results for Diophantine equations over finitely generated domains: A survey 63
10. On the optimal weight function in the Goldston–Pintz–Yıldırım method for finding small gaps between consecutive primes 75
11. Untangling upper-bound sieves 105
12. On a theorem of Erdős and Simonovits on graphs not containing the cube 113
13. A survey of Turán’s equivalent power series 127
14. Internal twists of L-functions 145
15. Turán’s new method and compressive sampling 155
16. Turán’s graph theorem, measures and probability theory 167
17. On the Turán–Kubilius inequality 177
18. Sums of a smooth number and a number with missing digits 187
19. Turán’swork in analytic number theory 205
20. On the irreducibility of basic automorphic representations 221
21. On composite rational functions 241
22. Some new results on gaps between consecutive primes 261
23. On some results of Turán about the local behavior of polynomials 279
24. On multiplicative decompositions of the set of the shifted quadratic residues modulo p 295
25. Paul Turán’s influence in combinatorics 309
26. On optimal interpolatory point systems 393
27. Paul Turán – A Capsule Biography 403