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: Mertens’ second theorem | Statement: [Mertens’ theorems, hasPart, Mertens’ second theorem]

Target entity: Mertens’ second theorem
Context triple: [Mertens’ theorems, hasPart, Mertens’ second theorem]

• A. Mertens’ theorems chosen
  Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
• B. Piatetski-Shapiro prime number theorem
  The Piatetski-Shapiro prime number theorem is a result in analytic number theory that establishes the existence of infinitely many primes among the values of certain non-integer power sequences, such as ⌊n^c⌋ for suitable real exponents c.
• C. Erdős–Wintner theorem
  The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
• 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. Dirichlet's theorem on arithmetic progressions
  Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.