TABLE O F CONTENT S
Preface vi i
Notation i x
Frequently use d Symbol s x i
Introduction xii i
Chapter I . Algebrai c an d Loca l Theorie s o f Generalize d
Unitary Group s 1
1. Elementar y propertie s o f hermitia n form s an d
unitary group s 1
2. Paraboli c subgroup s an d som e cose t decomposition s 7
3. Th e denominato r idea l o f a matri x 17
4. Hermitia n form s ove r a commutativ e semisimpl e algebr a
of rank 2 and quadrati c form s 2 3
5. Quadrati c an d hermitia n form s ove r a nonarchimedea n
local field 3 0
6. Unitar y group s ove r C 3 8
7. Symplecti c groups and split unitary groups over
local fields 4 8
Chapter II . Adelizatio n o f Algebrai c Group s an d Auto -
morphic Form s 5 7
8. Adelizatio n o f algebraic group s 5 7
9. Som e cose t decomposition s relativ e t o a paraboli c sub -
group 6 8
10. Automorphi c form s 7 5
11. Heck e operators i n a n arbitrar y grou p an d i n G ^ 8 3
12. Elementar y theor y o f Eisenstein serie s 9 2
Chapter III . Eule r Factor s o n Loca l Group s an d Eisen -
stein Serie s 101
13. Th e serie s a associate d wit h a hermitia n matri x 101
14. Th e serie s a^ wit h nonsingula r £ 109
15. Th e explici t for m o f OJ(0 , s) 118
16. Th e explici t for m o f a local Eule r facto r 125
17. Som e loca l grou p indice s 135
18. Eisenstei n serie s on G v 145
19. Th e pole s an d residue s o f Eisenstein serie s o n G v 157
Chapter IV . Mai n Theorem s o n Eule r Products , Eisen -
stein Series , an d th e Mas s Formul a 167
20. Mai n theorem s o n analyti c continuatio n 167
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