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Tau Conjecture

The tau conjecture, also known as Ramanujan's hypothesis after its proposer, states that

tau(n)∼O(n^(11/2+epsilon)),

where tau(n) is the tau function. This was proven by Deligne (1974) in the course of proving the more general Petersson conjecture. Deligne was awarded the Fields medal for his proof.

See also

Petersson Conjecture, Tau Function

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References

Apostol, T. M. Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 136 and 140, 1997.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, 1999.

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Tau Conjecture

Cite this as:

Weisstein, Eric W. "Tau Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TauConjecture.html

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