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2 fixed historical inaccuracy.

The logo for this year's ICM show the inequality $|\tau(n)| \leq n^{11/2} d(n)$ where $\sum \tau(n)q^n = q \prod_{n \neq 1} (1 - q^n)^{24}$ is the tau function. Wikipedia says this bound was conjectured by Ramanujan (appropriate for a conference in Hyderabad) and proven by Deligne in '74 in the process of proving as a corollary of the Weil Conjectures (which I also don't get). The background of the ICM logo looks like Ford circles (or sun rays). What is the hyperbolic geometry behind the Tau Conjecture and its proof?

EDIT: It would also be nice to see the proof of this bound, but the Weil conjectures and l-adic cohomology are a topic in themselves.

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# The geometry behind the ICM 2010 Logo

The logo for this year's ICM show the inequality $|\tau(n)| \leq n^{11/2} d(n)$ where $\sum \tau(n)q^n = q \prod_{n \neq 1} (1 - q^n)^{24}$ is the tau function. Wikipedia says this bound was conjectured by Ramanujan (appropriate for a conference in Hyderabad) and proven by Deligne in '74 in the process of proving the Weil Conjectures (which I also don't get). The background of the ICM logo looks like Ford circles (or sun rays). What is the hyperbolic geometry behind the Tau Conjecture and its proof?