Hadamard Factorization of the Xi Function
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\xi(s)=\frac{1}{2}\prod_\rho\left(1-\frac{s}{\rho}\right)
A common approach to studying the Riemann Zeta Function is to examine its counterpart, the Riemann Xi Function. Defined in the same 1859 paper, the Riemann Xi Function possesses additional regularity, which makes it more amenable to techniques from complex analysis.
With this in mind, one can see the utility of this product formula.
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