Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
positive integers
|
| gptkbp:field |
number theory
|
| gptkbp:firstAppearance |
1916
|
| gptkbp:form |
Δ(q) = q ∏_{n=1}^∞ (1 - q^n)^{24} = ∑_{n=1}^∞ τ(n)q^n
|
| gptkbp:hasConjecture |
gptkb:Ramanujan_conjectures
|
| gptkbp:hasSpecialCase |
τ(1) = 1
τ(10) = 115920 τ(2) = -24 τ(3) = 252 τ(4) = -1472 τ(5) = 4830 τ(6) = -6048 τ(7) = -16744 τ(8) = 84480 τ(9) = -113643 |
| https://www.w3.org/2000/01/rdf-schema#label |
Ramanujan's tau function
|
| gptkbp:level |
1
|
| gptkbp:modularForm |
Δ(z)
|
| gptkbp:multiplicative |
yes
|
| gptkbp:namedAfter |
gptkb:Srinivasa_Ramanujan
|
| gptkbp:originatedIn |
q-expansion of the discriminant modular form
|
| gptkbp:property |
multiplicative for coprime arguments
τ(p^{k+1}) = τ(p)τ(p^k) - p^{11}τ(p^{k-1}) for prime p |
| gptkbp:relatedTo |
modular forms
|
| gptkbp:sequence |
gptkb:A000594_(OEIS)
|
| gptkbp:symbol |
τ(n)
|
| gptkbp:type |
gptkb:cusp_form
|
| gptkbp:weight |
12
|
| gptkbp:bfsParent |
gptkb:Modular_forms
|
| gptkbp:bfsLayer |
6
|