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: Tauberian theorems | Statement: [analytic number theory, usesTool, Tauberian theorems]

Target entity: Tauberian theorems
Context triple: [analytic number theory, usesTool, Tauberian theorems]

• A. Tauberian theorems chosen
  Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
• B. Szegő limit theorem
  The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
• C. Abelian theorems
  Abelian theorems are results in mathematical analysis that deduce the behavior of a transformed function or series from known limiting behavior of the original one, typically in contrast to the inverse direction handled by Tauberian theorems.
• D. Herglotz functions
  Herglotz functions are analytic functions on the upper half-plane with nonnegative imaginary part, central in complex analysis and operator theory due to their integral representation and role in moment and interpolation problems.
• E. Fejér’s theorem on Fourier series
  Fejér’s theorem on Fourier series is a fundamental result in harmonic analysis stating that the Cesàro means (Fejér means) of the Fourier series of a continuous periodic function always converge uniformly to the function itself.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.