%A Zhishan YANG %T Ideal counting function in cubic fields %0 Journal Article %D 2017 %J Front. Math. China %J Frontiers of Mathematics in China %@ 1673-3452 %R 10.1007/s11464-016-0570-7 %P 981-992 %V 12 %N 4 %U {https://journal.hep.com.cn/fmc/EN/10.1007/s11464-016-0570-7 %8 2017-07-06 %X

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+n22xaK(n12+n22).