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Mean values connected with the Dedekind zeta-function of a non-normal cubic field

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Lü G.

Open Mathematics

2013

tom 11

nr 2

274-282

After Landau’s famous work, many authors contributed to some mean values connected with the Dedekind zetafunction. In this paper, we are interested in the integral power sums of the coefficients of the Dedekind zeta function of a non-normal cubic extension K 3/ℚ, i.e. $$ S_{l,K_3 } (x) = \sum\nolimits_{m \leqslant x} {M^l (m)} $$, where M(m) denotes the number of integral ideals of the field K 3 of norm m and l ∈ ℕ. We improve the previous results for $$ S_{2,K_3 } (x) $$ and $$ S_{3,K_3 } (x) $$.

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1 Open Mathematics

1 Lü G.

1 2013

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Mean values connected with the Dedekind zeta-function of a non-normal cubic field