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