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Accepted
A question about partial Euler products
This question turned out to be not too difficult. Please see
http://www.math.uic.edu/~rtakloo/euler-product.pdf
for a (casual) writeup of an answer.
Thanks for your comments and hints.
5
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3
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A question about partial Euler products
Let $K/{\mathbb Q}$ be an extension of degree $d$. Let $S$ be the set of primes $p$ which split completely in $K$. What can one say about the analytic properties of
$$
\zeta_{K, S}(s) : = \prod_{p \i …