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: Ramanujan expansions | Statement: [Ramanujan’s sum, usedFor, Ramanujan expansions]

Target entity: Ramanujan expansions
Context triple: [Ramanujan’s sum, usedFor, Ramanujan expansions]

• 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. Hardy–Ramanujan asymptotic formula
  The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
• C. Ramanujan theta function
  The Ramanujan theta function is a special type of q-series introduced by Srinivasa Ramanujan that plays a central role in the theory of modular forms, partitions, and mock theta functions.
• D. Ramanujan partition congruences
  Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
• E. Ramanujan’s lost notebook
  Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Ramanujan expansions
Triple: [Ramanujan’s sum, usedFor, Ramanujan expansions]

Ramanujan expansions are series representations of arithmetic functions expressed in terms of Ramanujan sums, analogous to Fourier expansions but over the integers.

Target entity: Ramanujan expansions
Target entity description: Ramanujan expansions are series representations of arithmetic functions expressed in terms of Ramanujan sums, analogous to Fourier expansions but over the integers.

• A. Ramanujan’s sum chosen
  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. Hardy–Ramanujan asymptotic formula
  The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
• C. Ramanujan theta function
  The Ramanujan theta function is a special type of q-series introduced by Srinivasa Ramanujan that plays a central role in the theory of modular forms, partitions, and mock theta functions.
• D. Ramanujan partition congruences
  Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
• E. Ramanujan’s lost notebook
  Ramanujan’s lost notebook is a posthumously discovered collection of Srinivasa Ramanujan’s final mathematical formulas and insights, many of which were decades ahead of their time in number theory and q-series.
• F. None of above.