Arithmetic Geometry.
This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with p-adic modular forms of half-integral weight and their roles in arithmetic geometry. T...
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| Format: | Electronic eBook |
| Language: | English |
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Providence :
American Mathematical Society,
1994
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| Series: | Contemporary Mathematics Ser.
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| Local Note: | ProQuest Ebook Central |
Table of Contents:
- Intro; Contents; Preface; Real Hilbertianity and the field of totally real numbers; Galois groups with prescribed ramification; Note on the zeros of p-adic L-functions; La fonction L p-adique de Kubota-Leopoldt; 1.
- Rappels.; 2.
- Quelques formules sur LÏ#x89;.; 2.1.
- Valeur de LÏ#x89; en Xâ#x80;#x93;jn pour j> 1; 2.2.
- Valeur de LÏ#x89; en Xâ#x80;#x93;jn pour j <0; 2.3.
- Valeur de LÏ#x89; en Xâ#x80;#x93;1n et en n; 3.
- Fonction de Kubota-Leopoldt.; 3.1.
- Définition.; 3.2.
- Valeurs de LKâ#x80;#x93;L en Xâ#x80;#x93;jn; 3.3.
- ""Conjecture"" principale.; 4.
- Cohomologie galoisienne.; 4.1.
- Notations.
- 4.2.
- Cohomologie galoisienne et dimensions4.3.
- Démonstrations par la méthode de Kolyvagin; 5.
- Conjectures sur les valeurs spéciales.; Supersingular p-adic height pairings on elliptic curves; Fields of definition of abelian varieties with real multiplication; p-adic interpolation of half-integral weight modular forms; 1. Introduction; 2. Definitions and properties; 2.1. p-adic modular forms; 2.2. The q-expansion principle; 2.3. Measures; 3. Interpolation; 3.1. The measure associated to a modular form; 3.2. Restriction of the measure to pZp; 4. Applications; References.
- Î#x9B;-adic modular forms of half-integral weight and a Î#x9B;-adic Shintani liftingThe non-existence of certain Galois extensions of Q unramified outside 2; Iwasawa theory and cyclotomic function fields; Slopes of modular forms; On the Taylor coefficients of theta functions of CM elliptic curves; 1. Introduction; 1.1. Acknowledgments; 2. Preliminaries; 2.1. Classical Modular Forms; 2.2. Formulaire Elliptique; 2.3. The Taylor coefficients of Îı; 3. Taylor Coefficients of Îı and Square Roots of Central Values; 3.1. The Elliptic Curves A(l); 3.2. The Formula; 4. Interpolation.
- 4.1. P-adic Modular Forms and Theta Measures4.2. P-adic Factorization Formulas; 4.3. P-adic Interpolation; 4.4. P-adic Îı; References; Torsion groups of elliptic curves over cubic and certain biquadratic number fields.
