Contribution Category

Divisor Functions

Divisor sums, convolution identities and arithmetic functions.

5 catalogue entries

5 entries shown from 177 detailed discovery and contribution-family records.

Divisor Functions

Divisor Functions

σ_{k} (n) = d ∣ n \sum d^{k}

Divisor Functions is catalogued as a function in Divisor Functions.

Level: Advanced
Source: Source catalogue
Status: needs-review

Open the entry for context, source notes, related formulas, and later mathematical developments.

Divisor Functions

Divisor-Sum Convolution Identities

Contribution family

Divisor-Sum Convolution Identities is catalogued as a identity in Divisor Functions.

Level: Advanced
Source: Source catalogue
Status: needs-review

Open the entry for context, source notes, related formulas, and later mathematical developments.

Divisor Functions

Divisor-Function Congruences

Contribution family

Divisor-Function Congruences is catalogued as a identity in Divisor Functions.

Level: Advanced
Source: Source catalogue
Status: needs-review

Open the entry for context, source notes, related formulas, and later mathematical developments.

Divisor Functions

Sums of Powers and Divisor Sums

Contribution family

Sums of Powers and Divisor Sums is catalogued as a identity in Divisor Functions.

Level: Advanced
Source: Source catalogue
Status: needs-review

Open the entry for context, source notes, related formulas, and later mathematical developments.

Divisor Functions

Sigma-Function Identities

σ_{k} (n) = d ∣ n \sum d^{k}

Sigma-Function Identities is catalogued as a identity in Divisor Functions.

Level: Advanced
Source: Source catalogue
Status: needs-review

Open the entry for context, source notes, related formulas, and later mathematical developments.

Archive Companion

Glossary

Namagiri DeviLanguage

The family deity Ramanujan revered. In the site, the term marks the devotional context he associated with mathematical insight.

Faith, Namakkal, goddess tradition

KumbakonamPlaces

The Tamil Nadu temple town where Ramanujan was raised, educated, married, and later died in 1920.

Town High School, notebooks, final years

ErodePlaces

Ramanujan's birthplace in present-day Tamil Nadu. He was born there on 22 December 1887.

Birthplace

MadrasPlaces

The colonial-era name for Chennai. Ramanujan worked around Madras before his Cambridge journey and had patrons there.

University of Madras, Port Trust

CambridgePlaces

The English university city where Ramanujan worked with G. H. Hardy at Trinity College from 1914 to 1919.

Hardy, Littlewood, Royal Society

PartitionMathematics

A way of writing a positive integer as a sum of positive integers where order is not counted separately.

p(n), congruences, asymptotic formula

CongruenceMathematics

A modular arithmetic relation saying two quantities leave the same remainder after division by a chosen modulus.

Partition congruences

Mock Theta FunctionMathematics

A mysterious q-series family from Ramanujan's final work, later understood through mock modular forms.

Lost Notebook, final letter

q-SeriesMathematics

A power series in the variable q. Ramanujan used q-series throughout his work on theta functions, products, and partitions.

Rogers-Ramanujan identities

Modular FormMathematics

A highly symmetric complex analytic function. Many later proofs of Ramanujan's results use modular forms.

Tau function, eta products

Srinivasa RamanujanPeople

Indian mathematician whose notebooks, formulas, and conjectures reshaped number theory, analysis, partitions, and q-series.

1887-1920

G. H. HardyPeople

Cambridge mathematician who recognized Ramanujan's genius, invited him to England, and collaborated with him.

Hardy-Ramanujan asymptotic formula

Janaki AmmalPeople

Ramanujan's wife, whose life intersected with his poverty, illness, separation during Cambridge years, and posthumous legacy.

Biography

NotebookConcepts

Ramanujan's handwritten collections of results, often stated without proofs and later studied by many mathematicians.

Three Notebooks, Lost Notebook

Lost NotebookConcepts

A manuscript collection rediscovered after Ramanujan's death, containing important late material including mock theta functions.

George Andrews, 1976 rediscovery

YantraLanguage

A sacred geometric diagram. Here it informs a restrained design vocabulary for mathematical symmetry and order.

Sacred geometry, mandala