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: Kummer sum | Statement: [Kummer, hasEponym, Kummer sum]

Target entity: Kummer sum
Context triple: [Kummer, hasEponym, Kummer sum]

• A. Gauss sum
  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. 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.
• C. Kummer congruences
  Kummer congruences are number-theoretic relations describing how special values of Bernoulli numbers and related arithmetic functions behave modulo powers of primes, foundational in the study of p-adic L-functions and cyclotomic fields.
• D. Ramanujan summation
  Ramanujan summation is a technique in mathematical analysis that assigns finite values to certain divergent series in a way consistent with analytic continuation and other regularization methods.
• E. Hurwitz zeta function
  The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Kummer sum
Target entity description: A Kummer sum is a type of exponential sum in number theory associated with the work of Ernst Kummer, often studied for its properties in modular arithmetic and cyclotomic fields.

• A. Gauss sum
  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. 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.
• C. Kummer congruences
  Kummer congruences are number-theoretic relations describing how special values of Bernoulli numbers and related arithmetic functions behave modulo powers of primes, foundational in the study of p-adic L-functions and cyclotomic fields.
• D. Ramanujan summation
  Ramanujan summation is a technique in mathematical analysis that assigns finite values to certain divergent series in a way consistent with analytic continuation and other regularization methods.
• E. Hurwitz zeta function
  The Hurwitz zeta function is a complex analytic function that generalizes the Riemann zeta function by introducing a shift parameter, playing a key role in analytic number theory and special function theory.
• F. None of above. chosen