According to this website, we see that Euler formally proved (observed?) his result connecting the harmonic series and a product over primes. Riemann wrote his historical paper in 1859 which considers the same observation, but now with $$\zeta(s)=\sum_{n=1}^\infty n^{-s}=\prod_p\left(1-p^{-s}\right)^{-1}$$where $s\in\Bbb C$. According to the same website above, it is said that Kronecker proved in 1876 the identity $\sum_{n=1}^\infty n^{-s}=\prod_p\left(1-p^{-s}\right)^{-1}$ for $s>1$. If this is the case, how well was Riemann's paper received by modern mathematicians at the time? It would seem to be based on something unproven. Or is it more likely something that all of the professional mathematicians would find obvious; hence, not worth publishing?

I've attempted to find some references regarding Kronecker, but MathSciNet didn't pull anything up (the publications jump from 1869 to 1881

According to this website, we see that Euler formally proved (observed?) his result connecting the harmonic series and a product over primes. Riemann wrote his historical paper in 1859 which considers the same observation, but now with $$\zeta(s)=\sum_{n=1}^\infty n^{-s}=\prod_p\left(1-p^{-s}\right)^{-1}$$where $s\in\Bbb C$. According to the same website above, it is said that Kronecker proved in 1876 the identity $\sum_{n=1}^\infty n^{-s}=\prod_p\left(1-p^{-s}\right)^{-1}$ for $s>1$. If this is the case, how well was Riemann's paper received by modern mathematicians at the time? It would seem to be based on something unproven. Or is it more likely something that all of the professional mathematicians would find obvious; hence, not worth publishing?

I've attempted to find some references regarding Kronecker, but MathSciNet didn't pull anything up (the publications jump from 1869 to 1881).