Hadamard Product for Riemann's Xi Function

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The discussion focuses on deriving the infinite product representation for Riemann's Xi function, expressed as Xi(s) = Γ(s/2)π^(-s/2)ζ(s). Participants are encouraged to manipulate the Hadamard product related to the zeta function to achieve this representation. The formula involves the product over complex zeros s_n of the zeta function, specifically using the structure of the product (∏_n (1 - s/s_n))/(s(s-1)). The conversation emphasizes the mathematical intricacies of connecting the Xi function to the properties of the zeta function. Overall, the thread highlights the relationship between these functions through the Hadamard product.
Charles49
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What is the infinite product for the function
\Xi(s)=\Gamma\left(\frac{s}{2}\right)\pi^{-s/2}\zeta(s)
?
 
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You can manipulate the Hadamard's zeta function infinite product to get your answer.
 
{\prod_n (1-s/s_n)\over s(s-1)}

where s_n is a complex zero of \zeta(s).
 
Thank you Avodyne
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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