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Note on the number of integral ideals in Galois extensions

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Abstract

Let K be an algebraic number field of finite degree over the rational filed ℚ. Let a k be the number of integral ideals in K with norm k. In this paper we study the l-th integral power sum of a k , i.e., Σk⩽α a l k (l = 2, 3, ...). We are able to improve the classical result of Chandrasekharan and Good. As an application we consider the number of solutions of polynomial congruences.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    GuangShi Lü

  2. Department of Mathematics, Capital Normal University, Beijing, 100048, China

    YongHui Wang

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  1. GuangShi Lü
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  2. YongHui Wang
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Correspondence to GuangShi Lü.

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Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

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Lü, G., Wang, Y. Note on the number of integral ideals in Galois extensions. Sci. China Math. 53, 2417–2424 (2010). https://doi.org/10.1007/s11425-010-4091-7

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  • DOI: https://doi.org/10.1007/s11425-010-4091-7

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