Introduction to Arithmetic Theory of Automorphic Functions Paperback - 1971
by Goro Shimura
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and, in particular, to elliptic modular forms with emphasis on their number-theoretical aspects.
First line
In this section we shall discuss some elementary properties of a group of transformations acting on a topological space.
From the rear cover
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem". Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Details
- Title Introduction to Arithmetic Theory of Automorphic Functions
- Author Goro Shimura
- Binding Paperback
- Pages 288
- Volumes 1
- Language ENG
- Publisher Princeton University Press, Princeton, NJ
- Date 1971-08-21
- ISBN 9780691080925 / 0691080925
- Weight 0.94 lbs (0.43 kg)
- Dimensions 8.98 x 6.28 x 0.69 in (22.81 x 15.95 x 1.75 cm)
- Library of Congress subjects Automorphic functions
- Library of Congress Catalog Number 94005898
- Dewey Decimal Code 515.9
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