Books by Irwin Kra

This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem.

There are incredibly rich connections between classical analysis and number theory. This title uncovers interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. It is suitable for a graduate course or for independent reading.

Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.