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Synopsis
Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'.
The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.
"synopsis" may belong to another edition of this title.
- PublisherBirkhäuser
- Publication date2018
- ISBN 10 331992706X
- ISBN 13 9783319927060
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages179
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Pseudodifferential Methods in Number Theory.
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Pseudodifferential Methods in Number Theory
Published by
Springer International Publishing Jul 2018, 2018
ISBN 10: 331992706X
ISBN 13: 9783319927060
New
Taschenbuch
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Classically developed as a tool for partial differential equations, theanalysis of operators known as pseudodifferential analysis is here regardedas a possible help in questions of arithmetic. The operators which make upthe main subject of the book can be characterized in terms of congruencearithmetic.They enjoy a Eulerian structure, and are applied to the searchfor new conditions equivalent to the Riemann hypothesis. These consist inthe validity of certain parameter-dependent estimates for a class of Hermitianforms of finite rank. The Littlewood criterion, involving sums ofMöbius coefficients, and the Weil so-called explicit formula, which leads tohis positivity criterion, fit within this scheme, using in the first case Weyl'spseudodifferential calculus, in the second case Fuchs'.The book should beof interest to people looking for new possible approaches to the Riemannhypothesis, also to new perspectives on pseudodifferential analysis and onthe way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions,no previous acquaintance is necessary. 180 pp. Englisch. Seller Inventory # 9783319927060
Quantity: 2 available
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Pseudodifferential Methods in Number Theory
Seller: Revaluation Books, Exeter, United Kingdom
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Paperback. Condition: Brand New. 180 pages. 9.45x6.61x0.47 inches. In Stock. Seller Inventory # x-331992706X
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