Introduction to Arithmetic Theory of Automorphic Functions
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A01=Goro Shimura
Abelian extension
Abelian variety
Abelian variety of CM-type
Algebra over a field
Algebraic closure
Algebraic curve
Algebraic extension
Algebraic function field
Algebraic group
Algebraic integer
Algebraic number field
Algebraically closed field
Allegory (category theory)
Analytic function
Author_Goro Shimura
Automorphic form
Automorphism
Category=PBK
Characteristic polynomial
CM-field
Coefficient
Commutative diagram
Complex conjugate
Complex multiplication
Complex number
Cusp form
Diagram (category theory)
Differential form
Dirichlet series
Division algebra
Divisor
Divisor (algebraic geometry)
Eisenstein series
Elliptic curve
Elliptic function
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler product
Existential quantification
Fuchsian group
Functional equation
Galois extension
Group homomorphism
Hecke operator
Homomorphism
Horsepower
Identity element
Inequality (mathematics)
Isogeny
Isomorphism class
Linear fractional transformation
Meromorphic function
Modular form
Module (mathematics)
Multiplication table
Natural number
Parity (mathematics)
Prime factor
Prime ideal
Prime number
Projection (mathematics)
Projective variety
Quadratic form
Quaternion algebra
Quotient space (linear algebra)
Rational number
Riemann surface
Ring (mathematics)
Simplicial complex
Soren Kierkegaard
Special case
Subgroup
Theorem
Triviality (mathematics)
Product details
- ISBN 9780691080925
- Weight: 425g
- Dimensions: 152 x 229mm
- Publication Date: 21 Aug 1971
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Goro Shimura is Professor of Mathematics at Princeton University.
