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