viii CONTENT S
4.5. Th e Jacquet-Langland s correspondenc e 5 0
4.6. Th e Shimura-Taniyama-Wei l conjecture , revisite d 5 1
4.7. Comple x multiplicatio n fo r / H/TN+^~ 5 1
4.8. Heegne r system s 5 2
4.9. Th e Gross-Zagie r formul a 5 3
References 5 4
Exercises 5 4
Chapter 5 . Rigi d analyti c modula r form s 5 7
5.1. p-adi c uniformisatio n 5 7
5.2. Rigi d analyti c modula r form s 6 0
5.3. p-adi c lin e integral s 6 3
Further result s 6 5
Exercises 6 5
Chapter 6 . Rigi d analyti c modula r parametrisation s 6 7
6.1. Rigi d analyti c modula r form s o n quaternio n algebra s 6 7
6.2. Th e Cerednik-Drinfel d theore m 6 8
6.3. Th e p-adic Shimura-Taniyama-Wei l conjectur e 6 8
6.4. Comple x multiplication , revisite d 6 9
6.5. A n example 7 0
6.6. p-adi c L-functions , d'apre s Schneider-Iovita-Spies s 7 3
6.7. A Gross-Zagie r formul a 7 4
Further result s 7 5
Exercises 7 5
Chapter 7 . Totall y rea l field s 7 9
7.1. Ellipti c curve s ove r numbe r field s 7 9
7.2. Hilber t modula r form s 8 0
7.3. Th e Shimura-Taniyama-Wei l conjectur e 8 2
7.4. Th e Eichler-Shimur a constructio n fo r totall y rea l field s 8 3
7.5. Th e Heegne r constructio n 8 4
7.6. A preview o f Chapte r 8 8 5
Further result s 8 6
Chapter 8 . AT R point s 8 7
8.1. Perio d integral s 8 7
8.2. Generalitie s o n grou p cohomolog y 8 8
8.3. Th e cohomolog y o f Hilbert modula r group s 8 9
8.4. AT R point s 9 3
References 9 5
Exercises 9 5
Chapter 9 . Integratio n o n H
p
x H 9 7
9.1. Discret e arithmeti c subgroup s o f SL 2(QP) x SL 2(M) 9 8
9.2. Form s o n H
p
x H 9 9
9.3. Period s 10
9.4. Som e p-adic cocycle s 104
9.5. Stark-Heegne r point s 105
9.6. Computin g Stark-Heegne r point s 106
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