Theta Functions, Kernel Functions, and Abelian Integrals.
- 1st ed.
- 1 online resource (119 pages)
- Memoirs of the American Mathematical Society ; v.1 .
- Memoirs of the American Mathematical Society .
Intro -- Table of Contents -- Introduction -- I. Review of the classical kernels -- II. Preliminaries on cross-cuts, periods, and the automorphic group -- III. The Klein prime function -- IV. Factorization theorems for differentials and Szegö kernels -- V. Existence proof for the classical Szegö kernel function -- VI. On the number of Szegö kernels -- VII. Some remarks on classical kernels and theta functions -- VIII. Kernels and Abelian differentials -- IX. Generalizations -- X. Some further identities -- XI. The elliptic case -- XII. A method of duality -- Addenda -- References.