Titlebook: Quantization and Arithmetic; André Unterberger Book 2008 Birkh?user Basel 2008 Matrix.Weyl calculus.calculus.coherent states.metaplectic r

貪婪性

Quantization, representation taken from the prolongation of the projective discrete series of representations of .(2,?) .When τ = -1/2, the representation in question is equivalent, under some intertwining, to the even part of the one-dimensional metaplectic representation, and that obtained when τ = 1/2 is equi

Ornament

Quantization and Modular Forms,to the representation .. The basic distribution . they are built from, substituting for the distributions δeven and δodd of Chapter 1, is just another realization of a modular form . of weight τ + 1 of some kind. Section 9 describes some possibilities: one may for instance consider a power of the De

迅速飛過

Back to the Weyl Calculus,it does not have to coincide with 4 or 12 any more. Then, not every element of (?/.?). is a square, and we have to consider the full set of distributions ?. as defined in Lemma 3.2: we introduce the linear combination . again a Γ-invariant distribution. Recall that ? is the set of squares in (?/.?).

ADOPT

機警

Jubilation

Book 2008r 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

resilience

Quantization and Modular Forms,ithmetic) coherent states for the representation π.+1 in the way described by a formula of resolution of the identity analogous to (1.2): note that the existence of such a formula depends in a crucial way on the fact that . is a cusp-form.

Outmoded

2297-0355 eared in Progress in Mathematics) by the same author: one-di(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)

evanescent

緩和