Tata lectures on Theta 1 1 /
The first of a series of three volumes surveying the theory of theta functions and its significance in the fields of representation theory and algebraic geometry, this volume deals with the basic theory of theta functions in one and several variables, and some of its number theoretic applications. R...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
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Boston :
Birkhäuser
c2007.
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| Edición: | 2nd ed |
| Colección: | Modern Birkhäuser classics.
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| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009461861506719 |
Tabla de Contenidos:
- CONTENTS; Introduction; Chapter I. Introduction and motivation: theta functions in one variable; 1. Definition of /&\Z,T) and its periodicity in z; 2. ^x,it) as the fundamental periodic solution to the Heat equation; 3. The Heisenberg group and theta functions with characteristics; 4. Projective embedding of (E/& + TLi by means of theta functions.; 5. Riemann's theta relations; 6. Doubly periodic meromorphic functions via ^KZ,T); 7. The functional equation of ^1(Z,T); 8. The Heat equation again; 9. The concept of modular forms; 10. The geometry of modular forms
- 11. /iP-as an automorphic form in 2 variables12. Interpretation of H/I\ as a moduli space; 13. Jacobi's derivative formula; 14. Product expansion of t£ and applications; 15. Representation of an integer as sum of squares; 16. Theta and Zeta; 17. Hurwitz maps; Appendix: Structure of the inverse limit J-£; 18. Hecke operators; References and Questions; Chapter II. Basic results on theta functions in several variables; 1. Definition of and its periodicity in z; 2. The Jacobian variety of a compact Riemann surface; 3. xP'and the function theory on a compact Riemann surface
- Appendix: The meaning of A4. Siegel's symplectic geometry; 5. tP'as a modular form; Appendix: Generators of Sp(2g,Z); 6. Riemann's theta formula and theta functions associated to a quadratic form; 7. Theta functions with harmonic coefficients
