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高斯域上离散数列短区间加权的Erd?s-Kac定理
Erd?s-Kac Theorem of Short Interval Weighting of Discrete Series on Gaussian Domain

DOI: 10.12677/pm.2026.161007, PP. 48-58

Keywords: Selberg-Delange方法,Erd?s-Kac定理,短区间
Selberg-Delange Method
, Erd?s-Kac Theorem, Short Interval

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Abstract:

设K是高斯域,aK(n)是 ?[ i ] 中范数为n的非零整理想的个数。本文建立了高斯域上离散数列短区间上以 a K ( n 2 ) l ( l∈ ? + ) 加权的Erd?s-Kac型定理,将使用推广的Selberg-Delange方法来研究此定理。
The Gaussian domain is the number of non-zero integer ideals in the middle norm. This article has established a high. The Erd?s-Kac type theorem, which is weighted by N on the short interval of discrete sequences on the Squain, will use the generalized. The Selberg-Delange method is used to study this theorem.

References

[1]  Landau, E. (1918) Einführung in die elementare und analytische theorie der algebraischen zahlen und der Ideale. BG Teubner.
[2]  Georg, W. (1993) On the Distribution of Integer Ideals in Algebraic Number Fields. Mathematische Nachrichten, 161, 59-74.
https://doi.org/10.1002/mana.19931610107
[3]  Chandrasekharan, K. and Good, A. (1983) On the Number of Integral Ideals in Galois Extensions. Monatshefte für Mathematik, 95, 99-109.
https://doi.org/10.1007/bf01323653
[4]  Zhai, W. (2015) Asymptotics for a Class of Arithmetic Functions. Acta Arithmetica, 170, 135-160.
https://doi.org/10.4064/aa170-2-3
[5]  Erdös, P. and Kac, M. (1939) On the Gaussian Law of Errors in the Theory of Additive Functions. Proceedings of the National Academy of Sciences, 25, 206-207.
https://doi.org/10.1073/pnas.25.4.206
[6]  Selberg, A. (1954) Note on a Paper by LG Sathe. Journal of the Indian Mathematical Society, 18, 83-87.
[7]  Delange, H. (1959) Sur des formules dues à Atle Selberg. Bulletin des Sciences Mathématiques, 83, 101-111.
[8]  Delange, H. (1971) Sur des formules de Atle Selberg. Acta Arithmetica, 19, 105-146.
https://doi.org/10.4064/aa-19-2-105-146
[9]  Tenenbaum, G. (2015) Introduction to Analytic and Probabilistic Number Theory. American Mathematical Society.
https://doi.org/10.1090/gsm/163
[10]  Lau, Y.K. and Wu, J. (2002) Sums of Some Multiplicative Functions over a Special Set of Integers. Acta Arithmetica, 101, 365-394.
https://doi.org/10.4064/aa101-4-5
[11]  Cui, Z., Lü, G. and Wu, J. (2018) The Selberg-Delange Method in Short Intervals with Some Applications. Science China Mathematics, 62, 447-468.
https://doi.org/10.1007/s11425-017-9172-7
[12]  Berndt, B.C. and Moree, P. (2025) Sums of Two Squares and the Tau-Function: Ramanujan’s Trail. Expositiones Mathematicae, 43, 125721.
https://doi.org/10.1016/j.exmath.2025.125721
[13]  Wu, J. and Wu, Q. (2020) Mean Values for a Class of Arithmetic Functions in Short Intervals. Mathematische Nachrichten, 293, 178-202.
https://doi.org/10.1002/mana.201800276
[14]  Labihi, O. and Raouj, A. (2020) Estimation de certaines sommes courtes. Journal of Number Theory, 206, 231-249.
https://doi.org/10.1016/j.jnt.2019.06.012
[15]  Wang, D. (2024) Weighted Erdős-Kac Type Theorems in Short Intervals. Acta Arithmetica, 212, 255-267.
https://doi.org/10.4064/aa230129-22-8

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