Hadamard Factorization Formula
\zeta(s)=\frac{(2\pi)^se^{-s-\frac{\gamma }{2}s}}{2(s-1)\Gamma\left(\frac{1}{2}s+1\right)}\prod_{p}\left(1-\frac{s}{\rho}\right)e^{\frac{s}{\rho}}
Hadamard’s factorization theorem allows us to express the Riemann zeta function as an infinite product over its non-trivial zeros. It also reflects deep connections between number theory and complex analysis.
This demonstration is quite complex. Before studying this proof, we recommend understanding the basic properties of the Zeta Function and the common arguments used in Analytical Number Theory.
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