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: Artin reciprocity law | Statement: [Artin’s conjecture on L-functions, relatedTo, Artin reciprocity law]

Target entity: Artin reciprocity law
Context triple: [Artin’s conjecture on L-functions, relatedTo, Artin reciprocity law]

• A. Artin reciprocity law chosen
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• B. 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.
• C. Artin’s conjecture on L-functions
  Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
• D. Chebotarev density theorem
  The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
• E. Furtwängler’s theorem in class field theory
  Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.