Anubhav Sharma ; Ayyadurai Sankaranarayanan
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On a general divisor problem related to a certain Dedekind zeta-function over a specific sequence of positive integers
We investigate the average behavior of coefficients of the Dirichlet series of positive integral power of the Dedekind zeta-function ζK3(s) of a non-normal cubic extension K3 of Q over a certain sequence of positive integers. More precisely, we prove an asymptotic formula with an error term for the sum∑a21+a22+a23+a24+a25+a26≤x(a1,a2,a3,a4,a5,a6)∈Z6ak,K3(a21+a22+a23+a24+a25+a26),