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: Möbius inversion formula | Statement: [Dirichlet convolution, relatedTo, Möbius inversion formula]

Target entity: Möbius inversion formula
Context triple: [Dirichlet convolution, relatedTo, Möbius inversion formula]

• A. Möbius function
  The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
• 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. Dirichlet convolution
  Dirichlet convolution is a binary operation on arithmetic functions that combines them via summation over divisors and plays a central role in multiplicative number theory and Dirichlet series.
• D. Mertens function
  The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Möbius inversion formula
Target entity description: The Möbius inversion formula is a fundamental result in number theory that allows one to recover an arithmetic function from its summatory function over divisors using the Möbius function.

• A. Möbius function
  The Möbius function is a multiplicative arithmetic function in number theory that assigns values based on the prime factorization of integers and plays a central role in inversion formulas and the study of prime distribution.
• 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. Dirichlet convolution
  Dirichlet convolution is a binary operation on arithmetic functions that combines them via summation over divisors and plays a central role in multiplicative number theory and Dirichlet series.
• D. Mertens function
  The Mertens function is an arithmetic function in number theory defined as the cumulative sum of the Möbius function, playing a key role in the study of the distribution of prime numbers and the Riemann Hypothesis.
• E. 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.
• F. None of above. chosen