Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:has_applications_in |
mathematical physics
|
| gptkbp:has_property |
tau(1) = 1
tau(n) is an integer for all n tau(n) is multiplicative tau(n) is related to the partition function tau(n) satisfies certain congruences |
| https://www.w3.org/2000/01/rdf-schema#label |
Ramanujan's tau function
|
| gptkbp:is_applied_in |
gptkb:crypt
|
| gptkbp:is_connected_to |
the theory of partitions
Hecke operators the Langlands program the theory of Galois representations the theory of modular forms and their applications in mathematical physics the theory of modular forms over p-adic fields the theory of modular forms and their applications in number theory |
| gptkbp:is_defined_by |
tau(n) = the coefficients of the q-expansion of the modular discriminant
all positive integers |
| gptkbp:is_expressed_in |
terms of modular forms
terms of theta functions terms of q-series terms of modular forms and their applications in number theory terms of Fourier coefficients terms of modular forms of higher level |
| gptkbp:is_part_of |
the theory of modular forms
the study of algebraic geometry the study of modular forms and their applications the study of modular forms and their applications in cryptography the study of number theory and algebra |
| gptkbp:is_related_to |
modular forms
L-functions the theory of modular equations the theory of special functions the theory of modular forms over finite fields the modularity theorem the theory of modular forms and their applications in algebraic geometry the Ramanujan conjecture the theory of elliptic curves over finite fields |
| gptkbp:is_studied_in |
algebraic number theory
|
| gptkbp:is_used_in |
number theory
the theory of elliptic curves the study of arithmetic geometry the study of automorphic forms the study of modular forms and their applications in physics the study of modular forms and their applications in arithmetic geometry the proof of Fermat's Last Theorem the study of modular invariants |
| gptkbp:named_after |
gptkb:Srinivasa_Ramanujan
|
| gptkbp:bfsParent |
gptkb:Srinivasa_Ramanujan
gptkb:R._Ramanujan |
| gptkbp:bfsLayer |
5
|