Automorphic Forms and the Picard Number of an Elliptic Surface

Automorphic Forms and the Picard Number of an Elliptic Surface

Automorphic Forms and the Picard Number of an Elliptic Surface by Peter F. Stiller

Contents of Automorphic Forms and Picard Number Elliptic Surface

  • PART 1. DIFFERENTIAL EQUATIONS
  • Generalities
  • Inhomogeneous equations
  • Automorphic forms
  • Periods
  • PART 2. K-EQUATIONS
  • Definitions
  • Local properties
  • Automorphic forms associated to K-equations and parabolic cohomology
  • PART 3. ELLIPTIC SURFACES
  • Automorphic forms and a result of Hoyt’s
  • Periods and the rank of Egen
  • A generalization
  • PART 4. HODGE THEORY
  • The filtrations
  • Differentials of the second kind
  • PART 5. THE PICARD NUMBER
  • Periods and period integrals
  • Periods and differential equations satisfied by normal functions
  • A formula, a method, and a remark on special values of Dirichlet series

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