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 sums | Statement: [Ernst Eduard Kummer, knownFor, Kummer sums]

Target entity: Kummer sums
Context triple: [Ernst Eduard Kummer, knownFor, Kummer sums]

• A. 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.
• B. Gaussian periods chosen
  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.
• C. Dedekind zeta functions
  Dedekind zeta functions are number-theoretic functions attached to algebraic number fields that encode their arithmetic properties, such as the distribution of prime ideals and class numbers.
• D. Dirichlet L-functions
  Dirichlet L-functions are complex analytic functions built from Dirichlet characters that generalize the Riemann zeta function and play a central role in number theory, particularly in the study of primes in arithmetic progressions.
• E. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.