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October 5th, 2018, 08:59 AM   #1
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Math Focus: algebraic number theory
Zeta functions of an extension of number fields

As it is known that the Zeta function of the quadratic number field can be expressed in terms of the Riemann Zeta function and a L function on the field of rationals Q.
Is this technique possible always for an extension L/K? can we always express the zeta function of L in term of the zeta and the L function of K (or, directly, of Q) ?
is there any results on this ? or any try for another particular cases?

Thank you for any help you can offer !
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