Duality in analytic number theory
by Elliott, P. D. T. A., (Peter D. T. A.)
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 applications, the book also illustrates a way of thinking mathematically: historical background in woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner…
Read More ↓Title Statements
- Full title :Duality in analytic number theory / P.D.T.A. Elliott.
Summary
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 applications, the book also illustrates a way of thinking mathematically: historical background in 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 arithmetic 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 individuals topics.
Edition Statements
- Publication Date:1997.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:1997.
The Physical Object
- Description:xviii, 341 pages ; : 24 cm
Edition Identifiers
- ISBN:0521560888, 9780521560887
- oclc:ocm33946909
- LC Classification:QA241
- Dewey Decimal:512/.73
Table of Contents
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 the class [actual symbol not reproducible]. A first application of the method -- 9. Multiplicative functions of the class [actual symbol not reproducible]: First Approach -- 10. Multiplicative functions of the class [actual symbol not reproducible]: Second Approach -- 11. Multiplicative functions of the class [actual symbol not reproducible]: 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.
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