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

Shimura, Goro

ISBN 10: 0691080925 / ISBN 13: 9780691080925

Published by Princeton University Press, 1971

About this Item

This item is in overall good condition. Covers and dust jackets are intact but may have minor wear including slight curls or bends to corners as well as cosmetic blemishes including stickers. Pages are intact but may have minor highlighting writing. Binding is intact; however, spine may have slight wear overall. Digital codes may not be included and have not been tested to be redeemable and or active. Minor shelf wear overall. Please note that all items are donated goods and are in used condition. Orders shipped Monday through Friday! Your purchase helps put people to work and learn life skills to reach their full potential. Orders shipped Monday through Friday. Your purchase helps put people to work and learn life skills to reach their full potential. Thank you!

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Bibliographic Details

• Title: Introduction to the Arithmetic Theory of Automorphic Functions (Publications of the Mathematical Society of Japan, Vol. 11)
• Publisher: Princeton University Press
• Publication Date: 1971
• Language: English
• ISBN 10: 0691080925
• ISBN 13: 9780691080925
• Binding: Soft cover
• Condition: good

About this title

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.

About the Author

Goro Shimura is Professor of Mathematics at Princeton University.