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Autor:
Iekata Shiokawa, Daniel Duverney
Publikováno v:
Monatshefte für Mathematik. 191:53-76
We give lower and upper bounds of the irrationality exponent of general continued fractions satisfying certain conditions. Using it we estimate the irrationality exponents of continued fractions representing numbers related with Cahen’s constant an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8c6f17ae63d3b7d55340991b65341d99
https://doi.org/10.1007/s00605-019-01335-0
https://doi.org/10.1007/s00605-019-01335-0
Publikováno v:
Mosc. J. Comb. Number Theory 8, no. 1 (2019), 57-69
Cahen’s constant is defined by the alternating sum of reciprocals of terms of Sylvester’s sequence minus 1. Davison and Shallit proved the transcendence of the constant and Becker improved it. In this paper, we study rationality of functions sati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d160d352cd078427692d2801aa29dac7
https://doi.org/10.2140/moscow.2019.8.57
https://doi.org/10.2140/moscow.2019.8.57
Publikováno v:
Tsukuba Journal of Mathematics. 44
Let $\{x_n\}$ be a sequence of rational numbers greater than one such that $x_{n+1} \geq x^2_n$ for all sufficiently large $n$ and let $\varepsilon_n \in \{-1,1\}$. Under certain growth conditions on the denominators of $x_{n+1}/x^2_n$ we prove that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b35534f2f3d1b80146796a4dd0a51d86
https://doi.org/10.21099/tkbjm/20204402235
https://doi.org/10.21099/tkbjm/20204402235
We state and prove three general formulas allowing to transform formal finite sums into formal continued fractions and apply them to generalize certain expansions in continued fractions given by Hone and Varona.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c941f0d450f43e8b8d2e58bdee0ec9f
Autor:
Takeshi Kurosawa, Iekata Shiokawa
Publikováno v:
Indagationes Mathematicae. 27:160-172
Let q ≥ 2 be an integer. We separate a given power series into q subseries according to the residue classes mod q of their powers. We study algebraic independence for values at an algebraic point of the q subseries of certain exponential power seri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::24b50a35634ac8adb6a0bd90c98f3f05
https://doi.org/10.1016/j.indag.2015.09.003
https://doi.org/10.1016/j.indag.2015.09.003
Autor:
Carsten Elsner, Iekata Shiokawa
Publikováno v:
The Ramanujan Journal. 29:273-294
Let P,Q, and R denote the Ramanujan Eisenstein series. We compute algebraic relations in terms of P(qi) (i=1,2,3,4), Q(qi) (i=1,2,3), and R(qi) (i=1,2,3). For complex algebraic numbers q with 0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::49e320c3c8849d0e2b252cb16cc920dc
https://doi.org/10.1007/s11139-012-9384-8
https://doi.org/10.1007/s11139-012-9384-8
Publikováno v:
Journal of Mathematical Sciences. 180:650-671
In this paper, we discuss the algebraic independence and algebraic relations, first, for reciprocal sums of even terms in Fibonacci numbers \( \sum\limits_{n = 1}^\infty {F_{2n}^{ - 2s}} \), and second, for sums of evenly even and unevenly even types
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9644ea0388d3bb3f2ce38c46fccf8de3
https://doi.org/10.1007/s10958-012-0663-0
https://doi.org/10.1007/s10958-012-0663-0
Autor:
Iekata Shiokawa, Yohei Tachiya
Publikováno v:
Acta Mathematica Hungarica. 132:190-206
We investigate linear relations between pattern sequences in a 〈q,r〉-numeration system, and give a basis of the module generated by pattern sequences for words of length not exceeding l. The expressions of pattern sequences using the basis are al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e281491994fb56cb9ecf35a638d8d23c
https://doi.org/10.1007/s10474-011-0082-6
https://doi.org/10.1007/s10474-011-0082-6
Publikováno v:
Acta Arithmetica. 148:205-223
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04d501fb6fb958b4e26c3d9609c0604a
https://doi.org/10.4064/aa148-3-1
https://doi.org/10.4064/aa148-3-1