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: Pólya–Vinogradov inequality | Statement: [analytic number theory, centralTheorem, Pólya–Vinogradov inequality]

Target entity: Pólya–Vinogradov inequality
Context triple: [analytic number theory, centralTheorem, Pólya–Vinogradov inequality]

• A. Bombieri–Vinogradov theorem
  The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
• B. Turán–Kubilius inequality
  The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
• C. Siegel–Walfisz theorem
  The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
• D. Chebyshev’s estimates for π(x)
  Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
• E. Linnik’s theorem on the least prime in an arithmetic progression
  Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Pólya–Vinogradov inequality
Target entity description: The Pólya–Vinogradov inequality is a fundamental result in analytic number theory that gives a strong upper bound on character sums, playing a key role in the study of Dirichlet characters and the distribution of primes in arithmetic progressions.

• A. Bombieri–Vinogradov theorem
  The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
• B. Turán–Kubilius inequality
  The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
• C. Siegel–Walfisz theorem
  The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
• D. Chebyshev’s estimates for π(x)
  Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
• E. Linnik’s theorem on the least prime in an arithmetic progression
  Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
• F. None of above. chosen