# Frontiers of Mathematics in China

 Front. Math. China    2017, Vol. 12 Issue (4) : 981-992     DOI: 10.1007/s11464-016-0570-7
 RESEARCH ARTICLE |
Ideal counting function in cubic fields
Zhishan YANG()
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
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 Abstract For a cubic algebraic extension K of ℚ, the behavior of the ideal counting function is considered in this paper. More precisely, let aK(n) be the number of integral ideals of the field K with norm n, we prove an asymptotic formula for the sum $∑n12+n22≤xaK(n12+n22).$ Corresponding Authors: Zhishan YANG Issue Date: 06 July 2017
 Cite this article: Zhishan YANG. Ideal counting function in cubic fields[J]. Front. Math. China, 2017, 12(4): 981-992. URL: http://journal.hep.com.cn/fmc/EN/10.1007/s11464-016-0570-7 http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/981