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17 reviews(Ebook) Tata Lectures on Theta I 1st Edition by David Mumford, C Musili, M Nori, E Previato, M Stillman - Ebook PDF Instant Download/Delivery: 9780817645724 ,0817645721
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Product details:
ISBN 10: 0817645721
ISBN 13: 9780817645724
Author: David Mumford, C Musili, M Nori, E Previato, M Stillman
(Ebook) Tata Lectures on Theta I 1st Edition Table of contents:
Definition of θ(Z, T) and its periodicity in z
θ(x, it) as the fundamental periodic solution to the heat equation
The Heisenberg group and theta functions with characteristics
Projective embedding of (E/ℤ + Tℒ) by means of theta functions
Riemann's theta relations
Doubly periodic meromorphic functions via θ(K, Z, T)
The functional equation of θ₁(Z, T)
The heat equation again
The concept of modular forms
The geometry of modular forms
θ₁ as an automorphic form in two variables
Interpretation of H/ℤ as a moduli space
Jacobi's derivative formula
Product expansion of θ₁ and applications
Theta functions as eigenfunctions of the Laplacian
Applications to number theory
Appendix: Modular forms and their applications
Introduction to several variables
Jacobian theta functions and their properties
Differential equations satisfied by theta functions
Theta functions and algebraic geometry
Applications to moduli spaces
Appendix: Further results and references
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Tags: David Mumford, C Musili, M Nori, E Previato, M Stillman, Tata Lectures
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