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Mathematics Lectures on modular functions of one complex variable (Tata Institute of Fundamental Research)
Posted on 2010-04-29
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More Lectures on modular functions of one complex variable (Tata Institute of Fundamental Research. Lectures on mathematics and physics. Mathematics, 29): Hans Maass Preface to the first edition: These are notes of lectures which I gave at the Tata Institute of Fundamental Research in 1962/63. They provide an introduction to the theory of modular functions and modular forms and may be described as elementary, in as much as basic facts from the theory of functions of a complex variable and some properties of the elementary transcendental functions form the only prerequisites. (It must be added that I have counted the Whittaker functions among the elementary transcendental functions). It seemed to me that the investigations of Siegel on discrete groups of motions of the hyperbolic plane with a fundamental region of finite volume form a particularly suitable introduction, since they make possible a simple characterization of groups conjugate to the modular group by a minimal condition.
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