Deza and Varukhina  established asymptotic formulae for some arithmetic functions in quadratic and cyclotomic fields. We generalize their results to any Galois extension of the rational field. During this process we rectify the main terms in their asymptotic formulae.
 Chandrasekharan, K., Narasimhan, R.1963The approximate functional equation for a class of zeta-functionsMath. Ann.15230–64.