# Journal of the Ramanujan Mathematical Society

Volume 38, Issue 2, June 2023 pp. 183–194.

On a divisor problem related to a certain Dedekind zeta-function

**Authors**:
Anubhav Sharma and Ayyadurai Sankaranarayanan

**Author institution:**
School of Mathematics and Statistics, University of Hyderabad Central University, P.O., Prof. C. R. Rao Road, Gachibowli,
Hyderabad 500 046, India.

**Summary: **
We consider the integral power sums of coefficients of the Dedekind zeta
function of a non-normal cubic extension K{3} of rational field Q given by
irreducible polynomial f (x) = x{3} + ax{2} + b{x} + c and prove
asymptotic formulae for ∑ n ≤ x a{k}, K{3} (n) with tightened error terms for k ≥ 2, where (ζK3 (s))k :=
∑ {∞} {n=1} {a{k}, K{3} (n)} / n{s}.

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