Synopsis
I. Differential Equations.- §1. Generalities.- §2. Inhomogeneous equations.- §3. Automorphic forms.- §4. Periods.- II. K-Equations.- §1. Definitions.- §2. Local properties.- §3. Automorphic forms associated to K-equations and parabolic cohomology.- III. Elliptic Surfaces.- §1. Introduction.- §2. A bound on the rank r of Egen (K(X)).- §3. Automorphic forms and a result of Hoyt's.- §4. Periods and the rank of Egen (K(X)).- §5. A generalization.- IV. Hodge Theory.- §1. The filtrations.- §2. Differentials of the second kind.- V. The Picard Number.- §1. Periods and period integrals.- §2. Periods and differential equations satisfied by normal functions.- §3. A formula, a method, and a remark on special values of Dirichlet series.- §4. Examples.- Appendix I. Third Order Differential Equations.
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