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Pure Mathematics 2025
Hurwitz连分数中误差和函数的若干性质
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Abstract:
对各类展式的误差和函数的研究从21世纪初就开始了，研究人员不断深入探讨其各种性质，如连续性、周期性、有界性、介值性等，同时给出函数图像的Hausdorff维数。在本文中，我们将探讨Hurwitz连分数的误差和函数，提出一些相关的性质，并研究其图像。
The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.
| [1] | Ridley, J.N. and Petruska, G. (2000) The Error-Sum Function of Continued Fractions. Indagationes Mathematicae, 11, 273-282. https://doi.org/10.1016/s0019-3577(00)89083-7 |
| [2] | 沈陆明, 王保伟. Lüroth误差和函数的若干性质[J]. 数学杂志, 2005, 25(3): 317-319. |
| [3] | Shen, L. and Wu, J. (2007) On the Error-Sum Function of Lüroth Series. Journal of Mathematical Analysis and Applications, 329, 1440-1445. https://doi.org/10.1016/j.jmaa.2006.07.049 |
| [4] | 沈陆明, 张继宏, 周建军. Engel展式误差和函数的若干性质(英文) [J]. 数学杂志, 2008, 28(1): 15-20. |
| [5] | 李伟, 周玉元, 桑宝祥, 等. Engel序列的误差和函数性质研究[J]. 四川理工学院学报(自然科学版), 2010, 23(6): 657-659. |
| [6] | Qiao, F. and Dai, M.F. (2010) On the Error-Sum Function of Expansion in Base P. International Journal of Nonlinear Science, 9, 330-334. |
| [7] | 马超, 谢启伟, 韩华. β展式的误差和函数[J]. 数学的实践与认识, 2011, 41(7): 235-238. |
| [8] | Jing, H. and Shen, L. (2012) Some Properties on the Error-Sum Function of Alternating Sylvester Series. Advances in Pure Mathematics, 2, 459-463. https://doi.org/10.4236/apm.2012.26070 |
| [9] | Chen, H., Wang, W. and Yu, M. (2014) Hausdorff Dimension of the Graph of the Error-Sum Function of \Alpha-Lüroth Series. Turkish Journal of Mathematics, 38, 803-811. https://doi.org/10.3906/mat-1309-63 |
| [10] | Ahn, M.W. (2023) On the Error-Sum Function of Pierce Expansions. Journal of Fractal Geometry, Mathematics of Fractals and Related Topics, 10, 389-421. https://doi.org/10.4171/jfg/142 |
| [11] | Robert, G.G. (2018) Complex Continued Fractions: Theoretical Aspects of Hurwitz’s Algorithm. Aarhus University. |
| [12] | Bugeaud, Y., Robert, G.G. and Hussain, M. (2023) Metrical Properties of Hurwitz Continued Fractions. |
