Ramanujan theta function

E355433

mathematical function q-series special 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.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Ramanujan theta function canonical	1
Ramanujan’s fifth order mock theta function χ1(q)	1
Ramanujan’s seventh order mock theta functions	1

How this entity was disambiguated

This entity first appeared as the object of triple T3410516 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Ramanujan theta function
Context triple: [Srinivasa Ramanujan, notableWork, Ramanujan theta function]

A. 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.
B. 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.
C. Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
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. Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Ramanujan theta function
Target entity description: 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.

A. 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.
B. 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.
C. Rogers–Ramanujan-type identities
Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
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. Jacobi’s four-square theorem
Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
F. None of above. chosen

Statements (45)

Predicate	Object
instanceOf	mathematical function ⓘ q-series ⓘ special function ⓘ
appearsIn	Ramanujan’s lost notebook ⓘ Ramanujan’s notebooks ⓘ linked to: Ramanujan’s lost notebook
convergesFor	\|q\| < 1 ⓘ
dependsOn	complex parameter q ⓘ complex variable z ⓘ
domain	complex numbers ⓘ
field	complex analysis ⓘ modular forms ⓘ number theory ⓘ partition theory ⓘ q-series theory ⓘ
generalizationOf	certain Jacobi theta functions ⓘ
hasProperty	admits product expansions ⓘ given by an infinite series in powers of q ⓘ holomorphic in z for fixed q with \|q\| < 1 ⓘ satisfies functional equations ⓘ
hasVariable	q ⓘ z ⓘ
introducedBy	Srinivasa Ramanujan ⓘ
introducedIn	early 20th century ⓘ
namedAfter	Srinivasa Ramanujan ⓘ
relatedTo	Dedekind eta function ⓘ Jacobi theta function ⓘ linked to: Jacobi theta functions mock theta function ⓘ modular equations ⓘ modular forms ⓘ modular group SL(2,Z) ⓘ linked to: SL(2,ℤ) q-Pochhammer symbol ⓘ q-hypergeometric series ⓘ
studiedBy	Bruce C. Berndt ⓘ G. N. Watson ⓘ George E. Andrews ⓘ
usedIn	Ramanujan’s congruences for partition function ⓘ linked to: Ramanujan partition congruences modular transformation formulas ⓘ q-series identities ⓘ theory of mock theta functions ⓘ theory of modular forms ⓘ theory of partitions ⓘ
usedToDefine	many mock theta functions ⓘ
usedToDerive	q-series transformation formulas ⓘ theta-type identities ⓘ
usedToExpress	partition generating functions ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Srinivasa Ramanujan → notableWork → Ramanujan theta function ⓘ

mock theta functions → hasExample → Ramanujan’s fifth order mock theta function χ1(q) ⓘ

linked to: Ramanujan theta function

mock theta functions → hasExample → Ramanujan’s seventh order mock theta functions ⓘ