國立虎尾科技大學 |

Pseudodifferential Methods in Number Theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Pseudodifferential Methods in Number Theory/ by André Unterberger.
作者:	Unterberger, André.
面頁冊數:	VI, 173 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Number theory. -
電子資源:	https://doi.org/10.1007/978-3-319-92707-7
ISBN:	9783319927077

Pseudodifferential Methods in Number Theory
Unterberger, André.

Pseudodifferential Methods in Number Theory[electronic resource] /by André Unterberger. - 1st ed. 2018. - VI, 173 p.online resource. - Pseudo-Differential Operators, Theory and Applications,132297-0355 ;. - Pseudo-Differential Operators, Theory and Applications,11.

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?

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.

ISBN: 9783319927077

Standard No.: 10.1007/978-3-319-92707-7doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241-247.5

Dewey Class. No.: 512.7

Pseudodifferential Methods in Number Theory
LDR:02822nam a22003975i 4500 001 989450
003 DE-He213
005 20200706020652.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319927077 $9 978-3-319-92707-7
024 7 $a 10.1007/978-3-319-92707-7 $2 doi
035 $a 978-3-319-92707-7
050 4 $a QA241-247.5
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.7 $2 23
100 1 $a Unterberger, André. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1266176
245 1 0 $a Pseudodifferential Methods in Number Theory $h [electronic resource] / $c by André Unterberger.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2018.
300 $a VI, 173 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Pseudo-Differential Operators, Theory and Applications, $x 2297-0355 ; $v 13
505 0 $a 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?
520 $a 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.
650 0 $a Number theory. $3 527883
650 0 $a Partial differential equations. $3 1102982
650 1 4 $a Number Theory. $3 672023
650 2 4 $a Partial Differential Equations. $3 671119
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319927060
776 0 8 $i Printed edition: $z 9783319927084
830 0 $a Pseudo-Differential Operators, Theory and Applications, $x 2297-0355 ; $v 11 $3 1266177
856 4 0 $u https://doi.org/10.1007/978-3-319-92707-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)