Tata Lectures on Theta II, Jacobian theta functions and differential equations by C. Musili, David Mumford, E. Previato, H. Umemura, M. Nori, M. Stillman

Tata Lectures on Theta II, Jacobian theta functions and differential equations



Download Tata Lectures on Theta II, Jacobian theta functions and differential equations




Tata Lectures on Theta II, Jacobian theta functions and differential equations C. Musili, David Mumford, E. Previato, H. Umemura, M. Nori, M. Stillman
Language: English
Page: 285
Format: djvu
ISBN: 0817645691, 9780817645694
Publisher: Birkhauser

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others.

A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries.

From the Back Cover

This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics.

Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).

Researchers and graduate students in mathematics and physics will find these volumes to be valuable additions to their libraries.


--This text refers to an alternate

edition.

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