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: Euler’s totient function | Statement: [Ramanujan’s sum, relatedTo, Euler’s totient function]

Target entity: Euler’s totient function
Context triple: [Ramanujan’s sum, relatedTo, Euler’s totient function]

• A. Euler’s totient function φ(n) chosen
  Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
• B. Dirichlet hyperbola method
  The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
• C. Jordan’s totient functions
  Jordan’s totient functions are a family of arithmetic functions in number theory that generalize Euler’s totient function to count k-tuples of integers modulo n with certain coprimality conditions.
• D. Ramanujan’s sum
  Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
• E. Euler’s theorem
  Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.