Quantization and Arithmetic

André Unterberger

ISBN 10: 3764387904 / ISBN 13: 9783764387907

Published by Birkhäuser, 2008

About this Item

Quantization and Arithmetic | André Unterberger | Taschenbuch | 147 S. | Englisch | 2008 | Birkhäuser | EAN 9783764387907 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 101852207

Bibliographic Details

• Title: Quantization and Arithmetic
• Publisher: Birkhäuser
• Publication Date: 2008
• Language: English
• ISBN 10: 3764387904
• ISBN 13: 9783764387907
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 170H x 9D millimeters 240 millimeters width by 170 millimeters height by 9 millimeters depth
• Weight: 284 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

(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