Automorphic Forms and the Reciprocity Law

Target entity: Automorphic Forms and the Reciprocity Law
Context triple: [Goro Shimura, notableWork, Automorphic Forms and the Reciprocity Law]

• A. Shimura reciprocity law
  The Shimura reciprocity law is a fundamental result in number theory that generalizes classical reciprocity laws by describing how values of modular functions at complex multiplication (CM) points transform under the action of Galois groups.
• B. Automorphic Forms and Representations
  Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
• C. Euler products for automorphic L-functions
  Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
• D. Hecke eigenforms
  Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
• E. Introduction to the Arithmetic Theory of Automorphic Functions
  Introduction to the Arithmetic Theory of Automorphic Functions is a foundational monograph by Goro Shimura that systematically develops the arithmetic aspects of automorphic forms and their connections to number theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Automorphic Forms and the Reciprocity Law
Target entity description: "Automorphic Forms and the Reciprocity Law" is a seminal mathematical work by Goro Shimura that develops deep connections between automorphic forms, number theory, and reciprocity laws in arithmetic geometry.

• A. Shimura reciprocity law
  The Shimura reciprocity law is a fundamental result in number theory that generalizes classical reciprocity laws by describing how values of modular functions at complex multiplication (CM) points transform under the action of Galois groups.
• B. Automorphic Forms and Representations
  Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
• C. Euler products for automorphic L-functions
  Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
• D. Hecke eigenforms
  Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
• E. Introduction to the Arithmetic Theory of Automorphic Functions
  Introduction to the Arithmetic Theory of Automorphic Functions is a foundational monograph by Goro Shimura that systematically develops the arithmetic aspects of automorphic forms and their connections to number theory.
• F. None of above. chosen