دانلود کتاب Lectures on Modular Forms. (AM-48), Volume 48

فهرست مطالب :

INTRODUCTION\nCONTENTS\nCHAPTER I. GEOMETRICAL BACKGROUND\n §1. Linear Fractional Transformations\n §2. The Modular Group\n §3. The Principal Congruence Subgroups\n §4. The Riemann Surfaces Associated to Subgroups of the Modular Group\n §5. Examples\nCHAPTER II. MODULAR FORMS\n §6. Introduction\n §7. A Review of Some Function Theory on Riemann Surfaces\n §8. The Dimension of the Space of Modular Forms\nCHAPTER III. POINCARÉ SERIES\n §9. Construction of Modular Forms\n §10. The Petersson Inner Product\n §11. Completeness of Poincaré Series\n §12. The Fourier Coefficients of Cusp Forms\nCHAPTER IV. EISENSTEIN SERIES\n §13. Construction of the Eisenstein Series.\n §14. The Fourier Coefficients of Eisenstein Series\n §15. The Modular Forms for the Modular Group\nCHAPTER V. MODULAR CORRESPONDENCES\n §16. The Hecke Operators\n §17. Hecke Operators and Fourier Coefficients\n §18. Arithmetic Properties of the Fourier Coefficients\nCHAPTER VI. QUADRATIC FORMS\n §19. Introduction\n §20. The Generalized Jacobi Inversion Formula\n §21. Representations by Sums of Squares\n §22. Even Integral Quadratic Forms\n §23. Arithmetic Applications