Theta Functions, Kernel Functions and Abelian Integrals

Download or read book Theta Functions, Kernel Functions and Abelian Integrals written by Dennis A. Hejhal and published by American Mathematical Soc.. This book was released on 1972 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents many interesting results, old and new, about theta functions, Abelian integrals and kernel functions on closed Riemann surfaces. It begins with a review of classical kernel function theory for plane domains. Next there is a discussion of function theory on closed Riemann surfaces, leading to explicit formulas for Szegö kernels in terms of the Klein prime function and theta functions. Later sections develop explicit relations between the classical Szegö and Bergman kernels and between the Szegö and modified (semi-exact) Bergman kernels. The author's results allow him to solve an open problem mentioned by L. Sario and K. Oikawa in 1969.