Anubhav Sharma ; Ayyadurai Sankaranarayanan - On a general divisor problem related to a certain Dedekind zeta-function over a specific sequence of positive integers

hrj:13033 - Hardy-Ramanujan Journal, February 11, 2024, Volume 46 - 2023 - https://doi.org/10.46298/hrj.2024.13033
On a general divisor problem related to a certain Dedekind zeta-function over a specific sequence of positive integersArticle

Authors: Anubhav Sharma 1; Ayyadurai Sankaranarayanan 2

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 suma21+a22+a23+a24+a25+a26x(a1,a2,a3,a4,a5,a6)Z6ak,K3(a21+a22+a23+a24+a25+a26),

where (ζK3(s))k:=n=1ak,K3(n)ns.


Volume: Volume 46 - 2023
Published on: February 11, 2024
Accepted on: February 11, 2024
Submitted on: February 9, 2024
Keywords: Dedekind zeta-function,Hecke eigenvalues,non-normal cubic extension,[MATH]Mathematics [math]

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