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Greg
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In his 1859 paper entitled "On the Number of Primes Less than a Given Magnitude", Riemann gives as his point of departure the equation
$$\prod\frac{1}{1-\frac{1}{p^s}}=\sum\frac{1}{n^s}$$[/size]
where $p$ is all primes and $n$ is all natural numbers. The function of the complex variable $s$, wherever these expressions converge, is called by Riemann $\zeta(s)$.
Any thoughts on how to prove this equation?
All comments welcome. :)
$$\prod\frac{1}{1-\frac{1}{p^s}}=\sum\frac{1}{n^s}$$[/size]
where $p$ is all primes and $n$ is all natural numbers. The function of the complex variable $s$, wherever these expressions converge, is called by Riemann $\zeta(s)$.
Any thoughts on how to prove this equation?
All comments welcome. :)