Automorphic Forms on GL(2) by H. Jacquet, R. P. Langlands

By H. Jacquet, R. P. Langlands

Show description

Read or Download Automorphic Forms on GL(2) PDF

Similar science & mathematics books

Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications: Proceedings of an Ams Special Session Held May 22-23, 1991 in

This booklet is the 1st set of complaints to be dedicated totally to the idea of hypergeometric capabilities outlined on domain names of positivity. lots of the clinical parts within which those capabilities are utilized contain analytic quantity thought, combinatorics, harmonic research, random walks, illustration conception, and mathematical physics---are represented the following.

Homotopy Theory of Function Spaces and Related Topics: Oberwolfach Workshop, April 5-11, 2009, Mathematisches Forschungsinstitut, Oberwolfach, Germany

Those 14 unique learn articles conceal localisation & rational homotopy concept, review subgroups, unfastened loop areas, Whitehead items, areas of algebraic maps, guage teams, loop teams, operads & string topology

Additional info for Automorphic Forms on GL(2)

Sample text

THOM introduced the spaces above in order to convert D,. into a stable homotopy group. We give now a bare outline of this noted theorem. 1) Thom. +k(MSO(k)), and m.. +k(MO(k)). The proof is long [40, 22]. Herewe merely define the isomorphisms. Suppose that M" is a closed oriented n-manifold. Embed M" in SnH via the Whitney embedding theorem. Denote by ~ : A -+ M" the normal cell bundle to M" in 5"+k. Assuming Sn+k oriented, we may assume the tangent bundle p, to Sn+k oriented; moreover the tangent bundle -r to Mn is oriented.

1) this is a monomorphism with image H .. (X, A; Z) ® QllcH.. o is a permanent cycle, so is every element of H7J(X,A ;Z) ® DaC H7l(X,A; Dq)· Now H7l(X, A; Z) ® Da is a direct summand of E;,q. the other summand TM being isomorphic to Tor(H'J)-l (X, A; Z), Da)· Since Da has no odd 42 II. Computation of the bordism groups torsion, Tv,a consists of 2-torsion only. 1), d 2 carries E~,q onto an odd torsion group, and since T v. a) = 0. Thus d2 = 0. As we continue through the spectral sequence, it is seen to be trivial.

Any Stiefel-Whitney dass of the product M: X vm is of form W; = 1 ® v1 + terms involving Stiefel-Whitney classes of M:. From dimensional considerations we see that W;, ... W;k(f;n)*cn,i = lt cn, i ® V;, ••• V;k' Thus N N (W;, ... W;k(l;n)*cn,i, an X am) N = = (I* (cn,i), an) (v;, ... V;k' am) (v;, ... = i, the Whitney numbers of the product associated with c"·; all vanish. Now suppose there is an expression Em,i [M:-m, 1;] 2 [V:'J 2 = 0. All the Whitney numbers must vanish. We show inductively that [V:'J 2 = 0 for all m, i.

Download PDF sample

Rated 4.26 of 5 – based on 17 votes