The Resource Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)
Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)
Resource Information
The item Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.This item is available to borrow from 1 library branch.
Resource Information
The item Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Bowdoin College Library.
This item is available to borrow from 1 library branch.
 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 parameterdependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coeffcients, and the Weil socalled 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
 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
 Label
 Pseudodifferential Methods in Number Theory
 Title
 Pseudodifferential Methods in Number Theory
 Statement of responsibility
 by André Unterberger
 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 parameterdependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coeffcients, and the Weil socalled 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
 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
 PseudoDifferential 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)
 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
 10.1007/9783319927077
 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)
 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
 10.1007/9783319927077
 Other physical details
 online resource
 Specific material designation
 remote
 System control number
 (WaSeSS)ssj0002038558
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bowdoin.edu/portal/PseudodifferentialMethodsinNumberTheoryby/LWxhG76gMjg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bowdoin.edu/portal/PseudodifferentialMethodsinNumberTheoryby/LWxhG76gMjg/">Pseudodifferential Methods in Number Theory, by André Unterberger, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bowdoin.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="https://link.bowdoin.edu/">Bowdoin College Library</a></span></span></span></span></div>