Lectures on Modular Functions of One Complex Variable
by H. Maass
Publisher: Tata institute of Fundamental Research 1983
Number of pages: 242
The book provides 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.
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by K. Ramachandra - Tata Institute of Fundamental Research
This short book is a text on the mean-value and omega theorems for the Riemann Zeta-function. The author includes discussion of some fundamental theorems on Titchmarsh series and applications, and Titchmarsh's Phenomenon.
by B. Malgrange - Tata Institute of Fundamental Research
Contents: Cauchy's formula and elementary consequences; Reinhardt domains and circular domains; Complex analytic manifolds; Analytic Continuation; Envelopes of Holomorphy; Domains of Holomorphy - Convexity Theory; d''-cohomology on the cube; etc.
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The text for advanced undergraduates and graduates, it offers a concise treatment, explanations, problems and solutions. Topics include elementary theory, general Cauchy theorem and applications, analytic functions, and prime number theorem.
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Several Complex Variables is a central area of mathematics with interactions with partial differential equations, algebraic geometry and differential geometry. This text emphasizes these interactions and concentrates on problems of current interest.