This volume aims to present a straightforward and easily accessible survey of the analytic theory of quadratic forms. Written at an elementary level, the book provides a sound basis from which the reader can study advanced works and undertake original research. Roughly half a century ago C.L. Siegel discovered a new type of automorphic forms in several variables in connection with his famous work on the analytic theory of quadratic forms. Since then Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the recent arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The text is based on the author's lectures given over a number of years and is intended for a one semester graduate course, although it can serve equally well for self study . The only prerequisites are a knowledge of algebra, number theory and complex analysis.
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"...an excellent introduction to the subject of Siegel modular forms written by an expert and can be recommended highly as a first text in the subject." Mathematical Reviews
Book Description
The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research.
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The symplectic group over R is a subgroup of the general linear group, defined by certain algebraic equations, and appears from there as an algebraic group. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
metrization theory, integral modular substitutions, cusp form with respect, automorphic form with respect, biholomorphic automorphisms, positive height, cusp forms, symplectic volume, integral columns, singular weight, modular forms, cocycle relation, modular group, integral entries, algebraic dependence, automorphic functions, reduction conditions, modular functions, fundamental domain, automorphic forms, discontinuous groups, maximal height, reduction theory, holomorphic functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Corollary Let, Lemma Let, Proof Let, Proof Note New!
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The symplectic group over R is a subgroup of the general linear group, defined by certain algebraic equations, and appears from there as an algebraic group. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
metrization theory, integral modular substitutions, cusp form with respect, automorphic form with respect, biholomorphic automorphisms, positive height, cusp forms, symplectic volume, integral columns, singular weight, modular forms, cocycle relation, modular group, integral entries, algebraic dependence, automorphic functions, reduction conditions, modular functions, fundamental domain, automorphic forms, discontinuous groups, maximal height, reduction theory, holomorphic functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Corollary Let, Lemma Let, Proof Let, Proof Note New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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2
books
cite this book:
- Number Theory for the Millennium Volume 1 by M.A. Bennett on page 125
- Elliptic Cohomology (University Series in Mathematics) by Charles B. Thomas in Back Matter
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