Tau Conjecture

Also known as Ramanujan's Hypothesis. Ramanujan proposed that

where is the Tau Function, defined by

This was proven by Deligne (1974), who was subsequently awarded the Fields Medal for his proof.

References

Deligne, P. La conjecture de Weil. I.'' Inst. Hautes Études Sci. Publ. Math. 43, 273-307, 1974.

Deligne, P. La conjecture de Weil. II.'' Inst. Hautes Études Sci. Publ. Math. 52, 137-252, 1980.

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 169, 1959.