Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11) - Softcover

Shimura, Goro

 
9780691080925: Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11)
Softcover
ISBN 10: 0691080925 ISBN 13: 9780691080925
Publisher: Princeton University Press, 1971

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

Goro Shimura is Professor of Mathematics at Princeton University.

From the Back 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.

"About this title" may belong to another edition of this title.

Publisher
Princeton University Press
Publication date
1971
Language
English
ISBN 10 
0691080925
ISBN 13 
9780691080925
Binding
Paperback
Number of pages
288