5.3. Euler' s summatio n o f the factoria l serie s 138
5.4. Th e genera l theor y o f summation o f divergen t serie s 145
5.5. Bore l summatio n 152
5.6. Tauberia n theorem s 158
5.7. Som e application s 163
5.8. Fourie r integral , Wiene r Tauberia n theorem , an d Gel'fan d
transform o n commutative Banac h algebra s 171
5.9. Generalize d function s an d smeare d summatio n 185
5.10. Gaussia n integrals , Wiene r measur e an d th e pat h integra l
formulae o f Feynman an d Ka c 191
Notes an d reference s 20 6
Chapter 6 . Eule r Product s 211
6.1. Euler' s produc t formul a fo r th e zet a functio n an d other s 211
6.2. Eule r product s fro m Dirichle t t o Heck e 217
6.3. Eule r product s fro m Ramanuja n an d Heck e to Langland s 23 8
6.4. Abelia n extension s an d clas s field theor y 25 1
6.5. Arti n nonabelia n L- functions 26 2
6.6. Th e Langland s progra m 26 4
Notes an d reference s 26 5
Gallery 26 9
Sample Page s fro m Opera Omnia 29 5
Index
301
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