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

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