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: Jacobi theta function | Statement: [Jacobi triple product, givesProductRepresentationOf, Jacobi theta function]

Target entity: Jacobi theta function
Context triple: [Jacobi triple product, givesProductRepresentationOf, Jacobi theta function]

• A. Jacobi theta functions chosen
  Jacobi theta functions are special functions in complex analysis and number theory that encode modular and elliptic properties, playing a central role in the theory of elliptic functions, modular forms, and various applications in mathematical physics.
• B. Riemann–Siegel theta function
  The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
• 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. Jacobi elliptic functions
  Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
• E. Jacobi triple product
  The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: givesProductRepresentationOf
Context triple: [Jacobi triple product, givesProductRepresentationOf, Jacobi theta function]

• A. componentRepresents
  Indicates that one component stands in for, symbolizes, or models another entity or concept within a system or context.
• B. representsAs
  Indicates that one entity serves as a depiction, symbol, or stand-in for another entity in some representational context.
• C. reducedRepresentationOf
  Indicates that one entity is a simplified, compressed, or lower-detail version of another entity while preserving its essential information or structure.
• D. hasRepresentationIn
  Indicates that one entity is represented, depicted, or encoded within another entity, such as a concept, object, or data structure having a corresponding representation in a specific medium or context.
• E. areRepresentedBy
  Indicates that one entity serves as a representation, proxy, or stand-in for another entity.
• F. None of above. chosen