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