This concise three-part therapy introduces undergraduate and graduate scholars to the speculation of automorphic features and discontinuous teams. writer Joseph Lehner starts via elaborating at the thought of discontinuous teams by way of the classical approach to Poincaré, using the version of the hyperbolic aircraft. the mandatory hyperbolic geometry is built within the textual content. bankruptcy develops automorphic services and varieties through the Poincaré sequence. formulation for divisors of a functionality and shape are proved and their effects analyzed. the ultimate bankruptcy is dedicated to the relationship among automorphic functionality concept and Riemann floor conception, concluding with a few functions of Riemann-Roch theorem.
The publication presupposes basically the standard first classes in advanced research, topology, and algebra. workouts diversity from regimen verifications to major theorems. Notes on the finish of every bankruptcy describe additional effects and extensions, and a thesaurus deals definitions of terms.
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