The Riemann Zeta Function

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Here is a view of the Riemann Zeta function graphed from x=1.2 to 10. You will notice a sharp spike as x goes toward 1, where it shoots off to infinity. The Riemann Zeta function at x=1 is the harmonic series. Since *everybody* knows the harmonic series diverges, so does the Riemann Zeta function at x=1. As x gets larger, the function approaches 1 quickly. This function directly determines the statistical properties of the distribution of prime numbers, so mathematician go wild studying everything about it.

gsl_sf_zeta.png
If you can prove that the only solutions to the equation Zeta(z) = 0 occur on the line Re(z) = 1/2 (aka The Riemann Hypothesis), then you get a million bucks!

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This page contains a single entry by Jonathan Leto published on September 7, 2008 2:08 PM.

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