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Duality in analytic number theory

Author: P D T A Elliott
Publisher: Cambridge : Cambridge University Press, 2008.
Series: Cambridge tracts in mathematics, 122.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

In this stimulating book, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory. He also illustrates a way of thinking  Read more...

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Document Type: Book
All Authors / Contributors: P D T A Elliott
ISBN: 9780521058087 0521058082
OCLC Number: 195748525
Notes: Originally published: 1997.
Description: pages cm.
Contents: 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 Halasz; 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. Ruckblick (after the manner of Johannes Brahms); References; Author index; Subject index.
Series Title: Cambridge tracts in mathematics, 122.
Responsibility: Peter D.T.A. Elliott.

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' ... a fruitful atempt in finding a general method in Analytic Number Theory.' Monatshefte fur Mathematik ' ... quite remarkable publication.' European Mathematical Society "The subject area of the Read more...

 
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