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: von Mangoldt function Λ(n) | Statement: [Chebyshev function ψ(x), expressibleVia, von Mangoldt function Λ(n)]

Target entity: von Mangoldt function Λ(n)
Context triple: [Chebyshev function ψ(x), expressibleVia, von Mangoldt function Λ(n)]

• A. Liouville function
  The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
• B. Chebyshev functions
  Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
• C. 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.
• D. Riemann zeta function
  The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
• E. Riemann–Siegel theta function
  The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: von Mangoldt function Λ(n)
Triple: [Chebyshev function ψ(x), expressibleVia, von Mangoldt function Λ(n)]

The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.

Target entity: von Mangoldt function Λ(n)
Target entity description: The von Mangoldt function Λ(n) is an arithmetic function in number theory that encodes the distribution of prime powers by assigning log p to integers n that are powers of a prime p and 0 otherwise.

• A. Liouville function
  The Liouville function is a completely multiplicative arithmetic function that assigns values based on the parity of the total number of prime factors of an integer, playing a key role in analytic number theory and the study of prime distribution.
• B. Chebyshev functions
  Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
• C. 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.
• D. Riemann zeta function
  The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
• E. Riemann–Siegel theta function
  The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
• F. None of above. chosen

Target predicate: expressibleVia
Context triple: [Chebyshev function ψ(x), expressibleVia, von Mangoldt function Λ(n)]

• A. expresses
  Indicates that one entity conveys, communicates, or articulates a thought, feeling, or idea through another medium or form.
• B. expressedThrough chosen
  Indicates that something (such as an idea, emotion, or content) is conveyed, manifested, or communicated by means of a particular medium, form, or channel.
• C. oftenExpressedAs
  Indicates that one thing is frequently represented, stated, or manifested in the form of another.
• D. cannotExpress
  Indicates that one entity is unable to convey, articulate, or communicate something (such as a feeling, idea, or message) to another entity.
• E. hasExpressivity
  Indicates that one entity possesses a certain level or type of expressive power, capability, or richness in representation relative to another.
• F. None of above.