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On the continued fraction expansions of some transcendental series in $\mathbb{F}_{q}((T^{-1}))$ | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، شماره 1، آبان 2026، صفحه 137-146 اصل مقاله (157.19 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.28559.1718 | ||
| نویسندگان | ||
| S. BELDI* ؛ F. Taktak | ||
| Lab. AGTS, University of Sfax, 3000 Sfax, Tunisia | ||
| چکیده | ||
| In this paper we describe the continued fraction expansions of certain infinite series over $\mathbb{F}_{q}(T)$, where $\mathbb{F}_{q}$ is a finite field with $q$ elements. As the first application, we determine the continued fraction expansion of the sum of rational functions with exponential elements. As the second application, we exhibit the continued fraction expansions of many classes of transcendental series that have bounded partial quotients. | ||
| کلیدواژهها | ||
| Continued fraction؛ Formal power series؛ Transcendance | ||
| مراجع | ||
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[1] B. Adamczewski and Y. Bugeaud, Palindromic continued fractions, Ann. Inst. Fourier, 57 (2007), 1557–1574. [2] J. P. Allouche, Sur la transcendance de la série formelle Π, Sém. Théorie des Nombres de Bordeaux, 2 (1990), 103–117. [3] J. P. Allouche, A. Lubiw, M. Mends̀France, A. J. van der Poorten and J. Shallit, Convergents of folded continued fractions, Acta Arith., 77 (1996), 77–96. [4] Kh. Ayadi, Ch. Ben Bechir and M. Saadaoui, Specializable series resulting from folded continued fractions and transcendence, Houston J. Math., 49 (2023), 339–351. [5] Kh. Ayadi, Ch. Ben Bechir and I. Elouaer, On some continued fractions and series, Stud. Sci. Math. Hungarica, (2) 58 (2021), 230–245. [6] T. Chaichana, V. Laohakosol and J. Rattanamoong, Continued fractions representing certain analogues of exponential elements in Fq((1/x)), East-West J. of Mathematics, 14(2012), 138–143. [7] A. Lasjaunias, Continued fractions for hyperquadratic power series over a finite field, Finite Fields Appl., 14 (2008), 329–350. [8] M. Mendès France, Sur les fractions continues limitées, Acta Arith., 23 (1973), 207–215. [9] A. J. van der Poorten and J. Shallit, Folded continued fractions, J. Number Theory, (2) 40 (1992), 237–250. [10] D. Thakur, Continued fraction for the exponential for Fq[T], J Number Theory, 41 (1992), 150–155. [11] D. Thakur, Exponential and continued fractions, J Number Theory, 59 (1996), 248–261. [12] D. Thakur, Patterns of continued fractions for the analogues of e and related numbers in function field case, J Number Theory, 66 (1997), 129–147. | ||
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