By David Soudry
ISBN-10: 0821825682
ISBN-13: 9780821825686
This paintings reports the neighborhood conception for convinced Rankin-Selberg convolutions for a standard functionality of measure of primary representations of over an area box. The neighborhood integrals converge in a half-plane and proceed meromorphically to the full airplane. One major result's the lifestyles of neighborhood gamma and components. The gamma issue is bought as a proportionality issue of a practical equation happy by means of the neighborhood integrals. moreover, Soudry establishes the multiplicativity of the gamma issue (first variable). a different case of this end result yields the unramified computation and includes a brand new proposal no longer provided ahead of. This presentation, which incorporates special proofs of the consequences, comes in handy to experts in automorphic types, illustration thought, and services, in addition to to these in different parts who desire to practice those effects or use them in different circumstances.
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Additional resources for Rankin-Selberg Convolutions for So2L+1 X Gln: Local Theory
Example text
M (t_ n)x (F) W ((™ I ) ) W r r(m)|detm|'+*-'d*rfm. 1) converges with £ = 0, for g in Levi (P*)), such that +(V, r) = /(tf)W„(r) ; y G F/, r € GI«(F) . Here / is a Schwartz function on 1/, to be chosen later. We have (denoting W* = W*,), for € > n * ( ( : /,-JA)=X/(»(: 0*'*)*- , w * = |detm|> /
2) f-f £? 2) is one of the integrals of the local theory for GL/(F) x GL n (F) (and its representation a ® r). I], the linear span of these integrals is the same as that of the A'(Wa, WTis). 3) is precisely A(WffiWT,cty s). 3. Assume that £ < n. 2. Here put for W„ € W(cr,tp) and WT € ^ ( r , ^ 1 ) , Af(W^WTls)= f Wa(m)WT(m Jzt\GU(F) \ )|detm|'-^c/m. "-l J l 36 DAVID SOUDRY Proposition. Given Wa G W{
Assume that £ < n. 2. Here put for W„ € W(cr,tp) and WT € ^ ( r , ^ 1 ) , Af(W^WTls)= f Wa(m)WT(m Jzt\GU(F) \ )|detm|'-^c/m. "-l J l 36 DAVID SOUDRY Proposition. Given Wa G W{
Rankin-Selberg Convolutions for So2L+1 X Gln: Local Theory by David Soudry
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