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The Resource Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)

Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)

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Summary
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 coeffcients, 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 diffculty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary
Language
eng
Work
Publication
Extent
1 online resource (VI, 173 p.)
Contents
  • Introduction - The basic tools
  • Some measures and distributions in the plane
  • Pseudodifferential arithmetic and Euler decompositions
  • The role of modular forms
  • Line measures and modular distributions
  • Arithmetic and the Fuchs calculus
  • A possible approach to the Riemann hypothesis?
Isbn
9783319927060
Instance
Label
Pseudodifferential Methods in Number Theory
Title
Pseudodifferential Methods in Number Theory
Statement of responsibility
by André Unterberger
Creator
Contributor
Subject
Language
eng
Summary
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 coeffcients, 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 diffculty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary
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Is part of
http://library.link/vocab/creatorName
Unterberger, André
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Pseudo-Differential Operators, Theory and Applications,
Series volume
13
http://library.link/vocab/subjectName
  • Mathematics
  • Differential equations, Partial
  • Number theory
Label
Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)
Instantiates
Publication
Contents
Introduction - The basic tools -- Some measures and distributions in the plane -- Pseudodifferential arithmetic and Euler decompositions -- The role of modular forms -- Line measures and modular distributions -- Arithmetic and the Fuchs calculus -- A possible approach to the Riemann hypothesis?
Control code
ssj0002038558
Dimensions
unknown
Extent
1 online resource (VI, 173 p.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9783319927060
Isbn Type
(print)
Other control number
10.1007/978-3-319-92707-7
Other physical details
online resource
Specific material designation
remote
System control number
(WaSeSS)ssj0002038558
Label
Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)
Publication
Contents
Introduction - The basic tools -- Some measures and distributions in the plane -- Pseudodifferential arithmetic and Euler decompositions -- The role of modular forms -- Line measures and modular distributions -- Arithmetic and the Fuchs calculus -- A possible approach to the Riemann hypothesis?
Control code
ssj0002038558
Dimensions
unknown
Extent
1 online resource (VI, 173 p.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9783319927060
Isbn Type
(print)
Other control number
10.1007/978-3-319-92707-7
Other physical details
online resource
Specific material designation
remote
System control number
(WaSeSS)ssj0002038558

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