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: Gauss sums | Statement: [Dirichlet characters, usedFor, Gauss sums]

Target entity: Gauss sums
Context triple: [Dirichlet characters, usedFor, Gauss sums]

• A. Gauss sum chosen
  A Gauss sum is a finite exponential sum, often involving characters such as the Legendre symbol, that plays a central role in number theory and the study of quadratic and higher-order residues.
• B. Jacobi sums
  Jacobi sums are special algebraic number theory constructs formed from character sums over finite fields or residue classes, widely used in primality testing and the study of cyclotomic fields.
• C. Gaussian periods
  Gaussian periods are special algebraic sums of roots of unity that play a key role in number theory, particularly in constructing regular polygons like the 17-gon with straightedge and compass and in understanding cyclotomic fields.
• D. Ramanujan’s sum
  Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.