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After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
- • uschian groups of the first kind • Automorphic forms and functions • Hecke operators and the zeta-functions associated with modular forms • Elliptic curves • Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves • Modular functions of higher level • Zeta-functions of algebraic curves and abelian varieties • The cohomology group assoicated with cusp forms • Arithmetic Fuschian groups
| Fachbereich: | Wahrscheinlichkeitstheorie |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 288 |
| ISBN-13: | 9780691080925 |
| ISBN-10: | 0691080925 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Shimura, Goro |
| Hersteller: | Princeton University Press |
| Maße: | 229 x 152 x 17 mm |
| Von/Mit: | Goro Shimura |
| Gewicht: | 0,471 kg |
- • uschian groups of the first kind • Automorphic forms and functions • Hecke operators and the zeta-functions associated with modular forms • Elliptic curves • Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves • Modular functions of higher level • Zeta-functions of algebraic curves and abelian varieties • The cohomology group assoicated with cusp forms • Arithmetic Fuschian groups
| Fachbereich: | Wahrscheinlichkeitstheorie |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 288 |
| ISBN-13: | 9780691080925 |
| ISBN-10: | 0691080925 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Shimura, Goro |
| Hersteller: | Princeton University Press |
| Maße: | 229 x 152 x 17 mm |
| Von/Mit: | Goro Shimura |
| Gewicht: | 0,471 kg |
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