TABLE O F CONTENT S
Chapters
I. Foundation s 1
1. Bilinea r Form s an d Presentation s o f Certai n 2-Ste p Nilpoten t Li e
Groups 1
2. Discret e Subgroup s o f th e Heisenber g Grou p 6
3. Th e Automorphis m Grou p o f th e Heisenber g Grou p lk
4. Fundamenta l Unitar y Representation s o f th e Heisenber g Grou p 17
5. Th e Fourie r Transfor m an d th e Weil-Brezi n Ma p 2 2
6. Distinguishe d Subspace s an d Lef t Actio n 3* +
II. Jacob i Thet a Function s an d th e Finit e Fourie r Transfor m kS
1. Nil-Thet a Function s an d Jacobi-Thet a Function s U 8
2. Th e Algebr a o f th e Finit e Fourie r Transfor m 6 0
III. Abelia n Varieties , Nil-Thet a an d Thet a Function s 6 9
1. A Genera l Constructio n an d Algebrai c Foundation s 6 9
2. Nil-Thet a Function s Associate d wit h a Positiv e Definit e H-morphis m
of a n Abelia n Variet y 8 3
3. Th e Relatio n Betwee n Nil-Thet a an d Classica l Thet a Function s 8 9
Bibliography 9 5
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