Theta Functions, Kernel Functions, and Abelian Integrals.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.