Higher moment of coefficients of Dedekind zeta function

Abstract

Let K₃ be a non-normal cubic extension over \mathbb{Q}.We study the higher moment of the coefficients aK₃ (n) of Dedekind zeta function over sum of two squares {\displaystyle {\sum }_{n_{\mathrm{1}}^{\mathrm{2}}+n_{\mathrm{2}}^{\mathrm{2}}\le x}{a}_{K_{\mathrm{3}}}^l(n_{\mathrm{1}}^{\mathrm{2}}+n_{\mathrm{2}}^{\mathrm{2}})},where 2≤l≤8 and n1,n2,l∈\mathbb{Z}.

Key words： Non-normal cubic field; Dedekind zeta function

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