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.

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