Talk:Dedekind zeta function

Artin L-function relationship

Some number theorist should correct the statement about factorization of Dedekind zeta(K) into Artin factors, since zeta(K) is defined for the absolute extension K/Q, not for an arbitrary extension L/K. Either relativize the definition of Dedekind function, or restrict the factorization formulas to K/Q.

Incorrect statement

In the "Euler product" section we have the following statement: "The fact that, for Re(s) > 1, ζ_K(s) is given by a product of non-zero numbers implies that it is non-zero in this region."

As worded, the statement is false. Many infinite products of non-zero numbers are zero. What is the correct statement? Ntsimp (talk) 23:28, 19 August 2016 (UTC)

@Ntsimp: Look here: The product is said to converge when the limit exists and is not zero. So the statement is correct since the product converges. --Jobu0101 (talk) 12:41, 4 September 2018 (UTC)

Dedekind zeta function associated to ideal classes

What about those? Can we discuss them here as well? --Jobu0101 (talk) 13:15, 4 September 2018 (UTC)

Unclear definition

The section Analytic continuation and functional equation contains this definition:

"$\Lambda _{K}(s)=\left|\Delta _{K}\right|^{s/2}\Gamma _{\mathbf {R} }(s)^{r_{1}}\Gamma _{\mathbf {C} }(s)^{r_{2}}\zeta _{K}(s)$"

But the article does not explain what $\left|\Delta _{K}\right|$ means, or provide a link for it, or give it a name so that it can be looked up. I hope someone knowledgeable about the subject will do so. 2601:200:C000:1A0:A4A6:107F:DACA:3489 (talk) 02:01, 26 June 2021 (UTC)