This quantity is the 1st of 3 in a sequence surveying the idea of theta services. in response to lectures given by way of the writer on the Tata Institute of basic study in Bombay, those volumes represent a scientific exposition of theta capabilities, starting with their ancient roots as analytic services in a single variable (Volume I), concerning many of the appealing methods they are often used to explain moduli areas (Volume II), and culminating in a methodical comparability of theta features in research, algebraic geometry, and illustration concept (Volume III).

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