Abstract
For a cubic algebraic extension K of ℚ, the behavior of the ideal counting function is considered in this paper. More precisely, let a K (n) be the number of integral ideals of the field K with norm n, we prove an asymptotic formula for the sum \(\sum\nolimits_{n_1^2 + n_2^2 \leqslant x} {a_K \left( {n_1^2 + n_2^2 } \right)} \).
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant No. 11526047).
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Yang, Z. Ideal counting function in cubic fields. Front. Math. China 12, 981–992 (2017). https://doi.org/10.1007/s11464-016-0570-7
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DOI: https://doi.org/10.1007/s11464-016-0570-7