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.
Criteria for independence, both algebraic and linear, are derived for continued fraction expansions of elements in the field
of Laurent series. These criteria are then applied to examples involving elements recently discovered to have explicit series
and continued fraction expansions.
We study two general divisor problems related to Hecke eigenvalues of classical holomorphic cusp forms, which have been considered by Fomenko, and by Kanemitsu, Sankaranarayanan and Tanigawa respectively. We improve previous results.