Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Taka Aki Tanaka"'
Publikováno v:
Tokyo Journal of Mathematics. 45
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b78c85c93d73a9e85519e617ff8562f3
https://doi.org/10.3836/tjm/1502179362
https://doi.org/10.3836/tjm/1502179362
Autor:
Yusuke Tanuma, Taka Aki Tanaka
Publikováno v:
International Journal of Number Theory. 14:2369-2384
We show that the Hecke–Mahler series, the generating function of the sequence [Formula: see text] for [Formula: see text] real, has the following property: Its values and its derivatives of any order, at any nonzero distinct algebraic numbers insid
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::838a87414d2555bf9fdc0e6757b3ab5d
https://doi.org/10.1142/s1793042118501440
https://doi.org/10.1142/s1793042118501440
Autor:
Akinari Goto, Taka Aki Tanaka
Publikováno v:
Journal of Number Theory. 184:384-410
We give positive characteristic analogues of complex entire functions having remarkable property that their values as well as their derivatives of any order at any nonzero algebraic numbers are algebraically independent. These results are obtained by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bd9a4cb3bb289221ec1dfc96a5a70aef
https://doi.org/10.1016/j.jnt.2017.08.026
https://doi.org/10.1016/j.jnt.2017.08.026
Publikováno v:
Acta Arithmetica. 168:161-186
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::48b1c5f2f394fbcc8998d116f9da81bc
https://doi.org/10.4064/aa168-2-5
https://doi.org/10.4064/aa168-2-5
Publikováno v:
Monatshefte für Mathematik. 174:77-104
In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec9e0a1f8fbaceb618ed74910a4dcb26
https://doi.org/10.1007/s00605-014-0617-3
https://doi.org/10.1007/s00605-014-0617-3
Publikováno v:
Tsukuba J. Math. 34, no. 2 (2011), 255-264
The aim of this paper is to establish necessary and sufficient conditions for certain infinite products generated by Fibonacci numbers and by Lucas numbers to be algebraically independent.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0257149f688e4b2eb35eb53c29fcb055
https://tsukuba.repo.nii.ac.jp/records/41606
https://tsukuba.repo.nii.ac.jp/records/41606
Autor:
Taka Aki Tanaka
Publikováno v:
Journal of Number Theory. 129:3081-3093
The main theorem of this paper, proved using Mahler's method, gives a necessary and sufficient condition for the values Θ ( x , a , q ) at any distinct algebraic points to be algebraically independent, where Θ ( x , a , q ) is an analogue of a cert
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c432cdb762974e32365cd04fb9a88932
https://doi.org/10.1016/j.jnt.2009.06.004
https://doi.org/10.1016/j.jnt.2009.06.004
Autor:
Taka Aki Tanaka
Publikováno v:
Results in Mathematics. 46:367-380
In this paper we establish, using Mahler’s method, the algebraic independence of the values at an algebraic number of power series closely related to decimal expansion of linearly independent positive numbers. First we consider a simpler case in Th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f61d2753d8f7d1088187164a22636c79
https://doi.org/10.1007/bf03322889
https://doi.org/10.1007/bf03322889
Publikováno v:
Monatshefte f�r Mathematik. 137:115-128
Suppose that {R n } n ⩾ 0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers $$$$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fd9e72532b7d873b4f370bc3f484e422
https://doi.org/10.1007/s00605-002-0501-4
https://doi.org/10.1007/s00605-002-0501-4
Autor:
Taka Aki Tanaka
Publikováno v:
Archiv der Mathematik. 78:202-209
Transcendence of the number \( \sum_{k=0}^\infty \alpha^{r_k} \), where \( \alpha \) is an algebraic number with 0 1 and \( \{r_k\}_{k\geqq0} \) is a sequence of positive integers such that \( \lim_{k\to\infty}\, r_{k+1}/r_k = d \in \mathbb{N}\, \bac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b34c60e2ca4756d2f536a83706dd6794
https://doi.org/10.1007/s00013-002-8237-x
https://doi.org/10.1007/s00013-002-8237-x