
Quantization and Arithmetic
André Unterberger(Author)
Birkhäuser (Publisher)
Published on 23. June 2008
Book
Paperback/Softback
147 pages
978-3-7643-8790-7 (ISBN)
Description
(12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. Consider on the line the distributions m (12) ? d (x)= ? (m)? x? , even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2 m?Z 2 i?x UnderaFouriertransformation,orundermultiplicationbythefunctionx ? e , the?rst(resp. second)ofthesedistributionsonlyundergoesmultiplicationbysome 24th (resp. 8th) root of unity. Then, consider the metaplectic representation Met, 2 a unitary representation in L (R) of the metaplectic group G, the twofold cover of the group G = SL(2,R), the de?nition of which will be recalled in Section 2: it extends as a representation in the spaceS (R) of tempered distributions. From what has just been said, if g ~ is a point of G lying above g? G,andif d = d even g ~ ?1 or d , the distribution d =Met(g~ )d only depends on the class of g in the odd homogeneousspace?\G=SL(2,Z)\G,uptomultiplicationbysomephasefactor, by which we mean any complex number of absolute value 1 depending only on g ~. On the other hand, a function u?S(R) is perfectly characterized by its scalar g ~ productsagainstthedistributionsd ,sinceonehasforsomeappropriateconstants C , C the identities 0 1 g ~ 2 2 | d ,u | dg = C u if u is even, 2 0 even L (R) ?\G
More details
Series
Edition
2008 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
147 p.
Dimensions
Height: 240 mm
Width: 170 mm
Thickness: 9 mm
Weight
284 gr
ISBN-13
978-3-7643-8790-7 (9783764387907)
DOI
10.1007/978-3-7643-8791-4
Schweitzer Classification
Other editions
Additional editions

André Unterberger
Quantization and Arithmetic
E-Book
09/2008
1st Edition
Birkhäuser
€53.49
Available for download
Content
Weyl Calculus and Arithmetic.- Quantization.- Quantization and Modular Forms.- Back to the Weyl Calculus.