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The Hyperbolic Laplace-Beltrami Operator

  • Markus Szymon Fraczek
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2139)

Abstract

In this chapter we will introduce some basic concepts of hyperbolic geometry and automorphic forms. A variety of books is available which provide a more comprehensive description of the relevant material. Hejhal’s books about the Selberg trace formula [58] and [59] are a source of exhaustive informations regarding most topics discussed in this chapter, these books are most useful for researches already familiar with most of the concepts. Iwaniec’s book [68] is more introductory in nature, discussing the relevant subjects in an accessible way. Bump’s book [25] covers both the classical and the representation theoretic views of automorphic forms. Bruggeman’s book on families of automorphic forms [21] is especially relevant in regard of deformations of automorphic forms, discussing their dependency on the weight and the character. For introductory articles on the spectral theory on hyperbolic surfaces and the Selberg trace formula see [14] and [83].

Keywords

Fundamental Domain Eisenstein Series Cusp Form Trace Formula Automorphic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Markus Szymon Fraczek
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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