Preface
Notation
Introduction
0. Duality and Fourier analysis
1. Background philosophy
2. Operator norm inequalities
3. Dual norm inequalities
4. Exercises: including the large sieve
5. The Method of the Stable Dual (1): deriving the approximate functional equations
6. The Method of the Stable Dual (2): solving the approximate functional equations
7. Exercises: almost linear, almost exponential
8. Additive functions of class La: a first application of the method
9. Multiplicative functions of the class La: first approach
10. Multiplicative functions of the class La: second approach
11. Multiplicative functions of the class La: third approach
12. Exercises: why the form? 13. Theorems of Wirsing and Halász
14. Again Wirsing's theorem
15. Exercises: the Prime Number Theorem
16. Finitely distributed additive functions
17. Multiplicative functions of the class La: mean value zero
18. Exercises: including logarithmic weights
19. Encounters with Ramanujan's function t(n)
20. The operator T on L2
21. The operator T on La and other spaces
22. Exercises: the operator D and differentiation
the operator T and the convergence of measures
23. Pause: towards the discrete derivative
24. Exercises: multiplicative functions on arithmetic progressions
Wiener phenomenon
25. Fractional power large sieves
operators involving primes
26. Exercises: probability seen from number theory
27. Additive functions on arithmetic progressions: small moduli
28. Additive functions on arithmetic progressions: large moduli
29. Exercises: maximal inequalities
30. Shifted operators and orthogonal duals
31. Differences of additive functions
local inequalities
32. Linear forms of additive functions in La
33. Exercises: stability
correlations of multiplicative functions
34. Further readings
35. Rückblick (after the manner of Johannes Brahms)
References
Author index
Subject index.
