This quantity is the 1st of 3 in a chain surveying the idea of theta services. in accordance with lectures given by means of the writer on the Tata Institute of basic examine in Bombay, those volumes represent a scientific exposition of theta capabilities, starting with their historic roots as analytic services in a single variable (Volume I), relating a number of the attractive 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 thought (Volume III).
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