Final Correspondence

Final Letter to Hardy on Mock Theta Functions

Mock theta functions enter mathematical history.

During his final period in India, Ramanujan wrote to Hardy about functions he called mock theta functions.

Ramanujan correspondence

Period

The letter belongs to Ramanujan's final period after his return to India.

Mock Theta Functions

Ramanujan introduced a class of q-series he called mock theta functions, whose transformation behaviour resisted immediate classification.

Later Interpretation

Mathematicians later connected these functions to mock modular forms and harmonic Maass forms.

Continued Importance

The subject remains important in number theory, combinatorics and mathematical physics.

Source Note

S. Ramanujan's final correspondence with G. H. Hardy concerning mock theta functions, 1920.

Example Mock Theta Notation