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Field name	Details
Dewey Class	515.984 (DDC 22)
Title	Tata Lectures on Theta I ([Ebook]) / David Mumford ; with the collaboration of C. Musili ... [et al.].
Author	Mumford, David , 1937-
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2007
Physical Details	: v.: digital
Series	Modern Birkhäuser classics
ISBN	9780817645779
Summary Note	CONTENTS; Introduction; Chapter I. Introduction and motivation: theta functions in one variable; 1. Definition of /&\Z,T) and its periodicity in z; 2. ^x,it) as the fundamental periodic solution to the Heat equation; 3. The Heisenberg group and theta functions with characteristics; 4. Projective embedding of (E/& + TLi by means of theta functions.; 5. Riemann's theta relations; 6. Doubly periodic meromorphic functions via ^KZ,T); 7. The functional equation of ^1(Z,T); 8. The Heat equation again; 9. The concept of modular forms; 10. The geometry of modular forms. 11. /iP-as an automorphic form in 2 variables12. Interpretation of H/I\ as a moduli space; 13. Jacobi's derivative formula; 14. Product expansion of t£ and applications; 15. Representation of an integer as sum of squares; 16. Theta and Zeta; 17. Hurwitz maps; Appendix: Structure of the inverse limit J-£; 18. Hecke operators; References and Questions; Chapter II. Basic results on theta functions in several variables; 1. Definition of and its periodicity in z; 2. The Jacobian variety of a compact Riemann surface; 3. xP'and the function theory on a compact Riemann surface. Appendix: The meaning of A4. Siegel's symplectic geometry; 5. tP'as a modular form; Appendix: Generators of Sp(2g,Z); 6. Riemann's theta formula and theta functions associated to a quadratic form; 7. Theta functions with harmonic coefficients:
System details note	Online access to this digital book is restricted to subscribing institutions through IP address (only for internal SISSA users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4577-9
Links to Related Works	Subject References: Algebraic Geometry . Functions of a Complex Variable . Functions of complex variables . Functions, Special . Functions, Theta . Geometry, Algebraic . History of mathematics . Number Theory . Authors: Mumford, David 1937- . Corporate Authors: SpringerLink (Online service) . Series: Modern Birkhäuser classics . Classification: 515.984 (DDC 22) .

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Tata Lectures on Theta I

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