Questions tagged [euler-product]

For questions on Euler products, an expansion of a Dirichlet series into an infinite product indexed by prime numbers.

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What can be said about $\prod_{s=2}^{\infty} \zeta(s)$?

Another problem from quora. What can be said about $v =\prod_{s=2}^{\infty} \zeta(s)$? Wolfy says that $v \approx 2.294856591673313794183$. The Inverse Symbolic Calculator (http://wayback.cecm....
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Permutation group of Satake parameters

Let $L(s)=\prod_{p}L_{p}(s)$ the Euler product of an L-function in the relevant right half-plane. As $L_{p}(s)=\prod_{j=1}^{d}(1-\alpha_{j}(p)p^{-s} )^{-1}$, the permutation group $G_{p}$ of the ...
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Why do you need to prove the error term goes to zero for the complete derivation of the Euler Product Formula?

I am doing a project on the Riemann-Zeta Function which begins by examining the Euler Product Formula. I understand the proof up until the point where it is made 'rigorous'. In other words, I ...
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Conditions of Euler Product

We know that if the infinite sum of a multiplicative function is absolute convergent, then the sum can be expressed as infinite product and the infinite product is absolutely convergent. Does there ...
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Surprising behavior of Leibniz formula for Pi (as Euler product)

I wrote a program to compute successive approximations of Pi using the following Euler product: π/4 = (3/4)*(5/4)*(7/8)*(11/12)*(13/12)... in which the ...
Euler product of $\sum (2^k n + 1)^{-s}$
do we know for a given $k > 2$ the Euler product of $\ \displaystyle\sum_{n=0}^\infty (2^k n + 1)^{\textstyle-s} \$ ? I saw that every prime numbers will appear in it, as well as some non-prime ...