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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+n22xaK(n12+n22).

Keywords Non-normal extension      ideal counting function      Rankin-Selberg convolution     
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
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