3
$\begingroup$

can the Euler product be defined on the critical line $ 1/2+it $ ??

i mean the Euler product for the Riemann Zeta function $$ \zeta(s)= \prod _{n}(1-p^{-s})^{-1} $$

for example from the representation of the Dirichlet generating function for the Rieman zeta would we have that ??

$$ \prod _{n\le x}(1-p^{-0.5-it})^{-1} =\exp\left(\sum_{n \le x}\frac{\Lambda(n)}{n^{0.5+it}}\right)$$

$\endgroup$
1
$\begingroup$

No. See https://mathoverflow.net/questions/63714/ ${ }$ ${ }$ ${ }$ ${ }$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.