Fundamental Domains and the Riemann Hypothesis

This book gathers together recent advances in geometric function theory, which made possible the proof of the Riemann Hypothesis. These advances have at their core the concept of fundamental domains, which originated in the theory of automorphic functions. Lars V. Ahlfors gave a broader meaning to this concept and emphasized its importance in the study of Riemann surfaces. The results of applying it to Blaschke products are remarkable and point to a natural extension of the concept of automorphic function. New and interesting facts are proved about arbitrary rational functions and in particular polynomials, as well as arbitrary transcendental functions, one of which is the Riemann Zeta function.

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Dorin Ghisa was born in 1940 in Romania. He graduated from the University Babes-Bolyai, Cluj with a degree in Mathematics and obtained his PhD degree in Complex Analysis at the University of Bucharest with the thesis "Quasi-Conformal Mappings on Riemann Surfaces." He has been a member of the AMS since 1981 and emeritus since 2011.