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

Guangshi Lü

Open Mathematics (2013)

  • Volume: 11, Issue: 2, page 274-282
  • ISSN: 2391-5455

Abstract

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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 ) = ∑ m ⩽ 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 ) .

How to cite

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Guangshi Lü. "Mean values connected with the Dedekind zeta-function of a non-normal cubic field." Open Mathematics 11.2 (2013): 274-282. <http://eudml.org/doc/269117>.

@article{GuangshiLü2013,
abstract = {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 \[ S\_\{3,K\_3 \} (x) \] .},
author = {Guangshi Lü},
journal = {Open Mathematics},
keywords = {Cusp form; Number field; Dedekind zeta function; cusp form; number field},
language = {eng},
number = {2},
pages = {274-282},
title = {Mean values connected with the Dedekind zeta-function of a non-normal cubic field},
url = {http://eudml.org/doc/269117},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Guangshi Lü
TI - Mean values connected with the Dedekind zeta-function of a non-normal cubic field
JO - Open Mathematics
PY - 2013
VL - 11
IS - 2
SP - 274
EP - 282
AB - 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 \[ S_{3,K_3 } (x) \] .
LA - eng
KW - Cusp form; Number field; Dedekind zeta function; cusp form; number field
UR - http://eudml.org/doc/269117
ER -

References

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