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portada Introduction to Arithmetic Theory of Automorphic Functions
Type
Physical Book
Year
1971
Language
English
Pages
288
Format
Paperback
ISBN
0691080925
ISBN13
9780691080925
Edition No.
1
Categories

Introduction to Arithmetic Theory of Automorphic Functions

Goro Shimura (Author) · Princeton University Press · Paperback

Introduction to Arithmetic Theory of Automorphic Functions - Goro Shimura

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£ 111.79

  • Condition: New
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Synopsis "Introduction to Arithmetic Theory of Automorphic Functions"

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.

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