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Cambridge Tracts in Mathematics Ser.: Duality in Analytic Number Theory by Peter D. T. A. Elliott (2008, Trade Paperback)

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Duality in Analytic Number Theory, Paperback by Elliott, P. D. T. A., ISBN 0521058082, ISBN-13 9780521058087, Brand New, Free shipping in the US Deals with analytic number theory; many new results.

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In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.

Product Identifiers

Publisher
Cambridge University Press
ISBN-10
0521058082
ISBN-13
9780521058087
eBay Product ID (ePID)
65620835

Product Key Features

Author
Peter D. T. A. Elliott
Publication Name
Duality in Analytic Number Theory
Format
Trade Paperback
Language
English
Publication Year
2008
Series
Cambridge Tracts in Mathematics Ser.
Type
Textbook
Number of Pages
360 Pages

Dimensions

Item Length
9in
Item Height
0.8in
Item Width
6in
Item Weight
20.5 Oz

Additional Product Features

Series Volume Number
Series Number 122
Lc Classification Number
Qa241 .E437 1997
Reviews
' ... a fruitful atempt in finding a general method in Analytic Number Theory.' Monatshefte für Mathematik, "The subject area of the book is one which is studied by relatively few specialists. However, given the widespread occurence of these ideas, this volume deserves a place in any library used by analytic number theorists." D.R. Heath-Brown, ' â€¦ a fruitful atempt in finding a general method in Analytic Number Theory.' Monatshefte fr Mathematik, ' ... a fruitful atempt in finding a general method in Analytic Number Theory.' Monatshefte f8r Mathematik
Table of Content
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.
Copyright Date
2008
Target Audience
Scholarly & Professional
Topic
Number Theory
Dewey Decimal
512.73
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics

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item 1 Duality in Analytic Number Theory, Paperback by Elliott, P. D. T. A., Like Ne...
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item 3 Duality in Analytic Number Theory (Cambridge Tracts in Mathematics), Elliott-,
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item 4 Duality in Analytic Number Theory: By P D T a Elliott, Peter D T a Elliott
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item 5 Duality in Analytic Number Theory by Peter D. Elliott (English) Paperback Book
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Cambridge Tracts in Mathematics Ser.: Duality in Analytic Number Theory by Peter D. T. A. Elliott (2008, Trade Paperback)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 Duality in Analytic Number Theory, Paperback by Elliott, P. D. T. A., Like Ne...

item 2 Duality in Analytic Number Theory, Paperback by Elliott, P. D. T. A., Brand N...

item 3 Duality in Analytic Number Theory (Cambridge Tracts in Mathematics), Elliott-,

item 4 Duality in Analytic Number Theory: By P D T a Elliott, Peter D T a Elliott

item 5 Duality in Analytic Number Theory by Peter D. Elliott (English) Paperback Book

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