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010   $a3-319-92707-8
024 7 $a10.1007/978-3-319-92707-7
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035   $a(DE-He213)978-3-319-92707-7
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035   $a(PPN)229503365
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100   $a20180716d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aPseudodifferential Methods in Number Theory /$fby André Unterberger
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018.
215   $a1 online resource (VI, 173 p.) 
225 1 $aPseudo-Differential Operators, Theory and Applications,$x2297-0355 ;$v13
311   $a3-319-92706-X 
327   $aIntroduction - 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?
330   $aClassically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coeffcients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no diffculty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.
410  0$aPseudo-Differential Operators, Theory and Applications,$x2297-0355 ;$v13
606   $aNumber theory
606   $aPartial differential equations
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
615  0$aNumber theory.
615  0$aPartial differential equations.
615 14$aNumber Theory.
615 24$aPartial Differential Equations.
676   $a512.7
700   $aUnterberger$b André$4aut$4http://id.loc.gov/vocabulary/relators/aut$0351381
906   $aBOOK
912   $a9910300135403321
996   $aPseudodifferential Methods in Number Theory$91563724
997   $aUNINA