Properties (45)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical function
|
| gptkbp:associated_with |
the study of congruences
|
| gptkbp:evaluates |
summation over roots of unity
|
| gptkbp:hasPrograms |
modular forms
two variables sums over roots of unity |
| https://www.w3.org/2000/01/rdf-schema#label |
Ramanujan's sum
|
| gptkbp:includes |
mathematical textbooks
|
| gptkbp:introduced |
gptkb:Srinivasa_Ramanujan
|
| gptkbp:is_a_subject_of |
research papers
abstract algebra advanced mathematics analytic number theory has historical significance in mathematics. |
| gptkbp:is_a_tool_for |
solving problems in number theory
solving_Diophantine_equations |
| gptkbp:is_essential_for |
the distribution of primes
the field of mathematics the study of prime numbers the study of modular forms and their properties |
| gptkbp:is_evaluated_by |
R(n, k) = Σ e^(2πi * j * k / n)
|
| gptkbp:is_involved_in |
generalized sums
|
| gptkbp:is_part_of |
gptkb:Ramanujan's_work_on_partitions
Ramanujan's_legacy |
| gptkbp:is_recognized_for |
positive integers
any integer n and k |
| gptkbp:is_studied_in |
mathematicians worldwide
arithmetic functions analytic combinatorics |
| gptkbp:is_used_in |
cryptography
theoretical physics analytic number theory the prime number theorem |
| gptkbp:isConnectedTo |
Fourier analysis
modular arithmetic |
| gptkbp:isUsedFor |
asymptotic formulas
|
| gptkbp:related_to |
number theory
the theory of modular forms L-functions the Riemann zeta function the divisor function the distribution of arithmetic functions |
| gptkbp:standardFeatures |
Dirichlet characters
|
| gptkbp:suitableFor |
signal processing
|
| gptkbp:symbolizes |
R(n, k)
|