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: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" | Statement: [Vinogradov's three-primes theorem, appearsIn, Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"]

Target entity: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"
Context triple: [Vinogradov's three-primes theorem, appearsIn, Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"]

• A. Vinogradov's three-primes theorem
  Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
• B. Trigonometric Series, Vol. I
  Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
• C. Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
  Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
• D. van der Corput method for estimating exponential sums
  The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
• E. Trigonometric Series, Vol. II
  "Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers"
Target entity description: Vinogradov's book "The Method of Trigonometrical Sums in the Theory of Numbers" is a classic monograph in analytic number theory that develops powerful techniques of trigonometric (exponential) sums to tackle additive problems, including results on the representation of integers as sums of primes.

• A. Vinogradov's three-primes theorem
  Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
• B. Trigonometric Series, Vol. I
  Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
• C. Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
  Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
• D. van der Corput method for estimating exponential sums
  The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
• E. Trigonometric Series, Vol. II
  "Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
• F. None of above. chosen