Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11) (Publications of the Mathematical Society of Japan, No 11) - Tapa blanda

Shimura, Goro

 
9780691080925: Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11) (Publications of the Mathematical Society of Japan, No 11)
Tapa blanda
ISBN 10: 0691080925 ISBN 13: 9780691080925
Editorial: Princeton University Press, 1971

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Goro Shimura is Professor of Mathematics at Princeton University.

De la contraportada

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Princeton University Press
Año de publicación
1971
Idioma
Inglés
ISBN 10 
0691080925
ISBN 13 
9780691080925
Encuadernación
Tapa blanda
Número de páginas
288
Contacto del fabricante
no disponible
Persona responsable
no disponible