Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Automorphic Forms and the Reciprocity Law | Statement: [Goro Shimura, notableWork, 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