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Function theory

Introduction

The central concern of this presentation of the classical mathematical discipline of function theory is to advance quickly to the central sentences with the least possible amount of terminology. The first four chapters contain a comparatively simple introduction to the function theory of a complex variable and culminate in the proof of the small Riemann mapping theorem and a characterization of simply connected areas. Further topics covered are: - The theory of elliptic functions based on the model of K. Weierstrass. (With an excursus about the older approach (N.H. Abel, C.G.F. Jacobi) about the theta functions); - a systematic continuation of the theory of module functions and module forms; - Applications of function theory to analytical number theory; - the proof of the prime number theorem with a weak form of the remainder. Factual motivation, an unusually large number of exercises in each chapter, historical notes and numerous illustrations make the presentation particularly attractive. The structuring of the text in chapter summaries and special emphasis makes it easier for the reader to find his way around and makes this textbook well suited for self-study and for exam preparation.
The present third edition has been expanded to include a list of symbols and has been improved in various places.

Keywords

Differential equation Elliptical functions Elliptical modular forms Function theory Minimum modular form analytical number theory

Authors and affiliations

  • Eberhard Friday
  • Rolf Busam
  1. 1. Mathematical InstituteRuprecht-Karls-Universit├Ąt HeidelbergHeidelbergGermany

Bibliographic information

  • Book Title Function Theory
  • AuthorsEberhard Friday
    Rolf Busam
  • Series TitleSpringer Textbook
  • DOIhttps: //doi.org/10.1007/978-3-662-07352-0
  • Copyright InformationSpringer-Verlag Berlin Heidelberg2000
  • Publisher NameSpringer, Berlin, Heidelberg
  • eBook PackagesSpringer Book Archive
  • Softcover ISBN978-3-540-67641-6
  • eBook ISBN978-3-662-07352-0
  • Series ISSN0937-7433
  • Edition Number3
  • Number of PagesXX, 541
  • Number of Illustrations71 b / w illustrations, 0 illustrations in color
  • TopicsAnalysis
  • Buy this book on publisher's site