Tanaka, Takaaki

Last updated: May 29, 2019 at 03:54

Name	Tanaka, Takaaki
E-mail	takaakimath.keio.ac.jp
URL	http://www.math.keio.ac.jp/~takaaki/
Affiliation	Keio University
Section	Faculty of Science and Technology Department of Mathematics
Job title	Associate Professor
Degree	博士（理学）(Keio University)
Research funding number	60306850

Research Interests

algebraic independence(2) , transcendental numbers(1)

Research Areas

Mathematics / Algebra / Analytic Number Theory

Academic & Professional Experience

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Apr 1996

Mar 1998

日本学術振興会 ,特別研究員

Apr 1998

Mar 2007

慶應義塾大学（理工学部）,助手

Feb 2001

Mar 2002

フンボルト財団（ドイツ連邦共和国，ケルン大学） ,奨学研究員

Apr 2006

Mar 2009

慶應義塾大学（経済学部）,非常勤講師

Apr 2007

Mar 2010

慶應義塾大学（理工学部）,助教

Education

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Mar 1993

数理科学科, Faculty of Science and Engineering, Keio University

Mar 1995

数理科学専攻, Graduate School, Division of Science and Engineeri, Keio University

Mar 1998

数理科学専攻, Graduate School, Division of Science and Engineeri, Keio University

Published Papers

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Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers

Tanaka, Taka-aki, Tanuma, Yusuke

Int. J. Number Theory 14 2369-2384 Oct 2018 [Refereed]

Hecke-Mahler series is the generating function of the sequence {[nω]} of the integral parts [nω] of the positive integer multiple nω for ω real. In this paper, we prove that the Hecke-Mahler series has the following property: Its values and its de...

Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field

Goto, Akinari, Tanaka Taka-aki

J. Number Theory 184 384-410 Mar 2018 [Refereed]

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...

Explicite algebraic dependence formulae of infinite products related with Fibonacci and Lucas numbers

Kaneko, H., Kurosawa, T., Tachiya, Y., and Tanaka Taka-aki

Acta Arithmetica 168(2) 161-186 Apr 2015 [Refereed]

Arithmetic properties of solutions of certain functional equations with transformations represented by matrices including a negative entry

Tanaka, Taka-aki

Tokyo J. Math. 37(1) 211-223 Jun 2014 [Refereed]

Mahler関数において変数の変換を表す行列は非負行列に限る、という従来の制約の外にある多変数Mahler関数の新しいクラスについてその値の代数的独立性を示し、2項回帰数列で生成されるLaurent級数の値の代数的独立性を証明した。

Algebraic independence results for the values of certain Mahler functions and their application to infinite products

Kurosawa, T., Tachiya, Y., Tanaka, Taka-aki

Monatsh. Math. 174(1) 77-104 May 2014 [Refereed]

無限積表示される整関数であって零点以外の相異なる代数的数における値及びそれら代数的数における逐次微分をすべて併せた無限集合が代数的独立となるものを、2項回帰数列の等比数列に対応する部分列を用いて構成した。これを達成するため多変数Mahler関数の特殊値の新たな代数的独立性判定定理を証明した。

Conference Activities & Talks

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Algebraic independence properties of a certain map defined on the set of orbits of the action of Klein four-group

TANAKA TAKA-AKI

Keio-Yonsei Number Theory Workshop 4 Dec 2018

In the previous work the speaker constructed a function of two variables taking algebraically independent values at any distinct points belonging to the cartesian product of the set of nonzero algebraic numbers and that of nonzero algebraic number...

Algebraic independence of the values of a certain map defined on the set of orbits of the action of Klein four-group [Invited]

TANAKA TAKA-AKI

Analytic Number Theory and Related Topics 31 Oct 2018 Research Institute for Mathematical Sciences

先行研究において講演者は、0以外の代数的数全体と単位円内の0でない代数的数全体の直積集合に属する任意の相異なる点における値がすべて代数的独立となる２変数関数を構成した。本講演では、上記の２変数関数にある種のバランス化を施し、定義域を複素数全体と単位円周を除く複素数全体の直積集合に拡張した関数を紹介する。この関数は定義域に対するクラインの４元群の作用に関する軌道全体の集合上で定義された写像とも見做すことができ、この写像は代数点に代表される任意の相異なる軌道における値がすべて代数的独立となる。

On the functions having `perfect' algebraic independence property at algebraic numbers

Taka-aki Tanaka

Diophantine Analysis and Related Fields 2017 7 Jan 2017 Nihon Univ.

有限個の素数pに対するQpとRの`共通部分'に属する超越数から成る代数的独立な無限集合について

Taka-aki Tanaka, Miho Nakashima

日本数学会年会 18 Mar 2016

Algebraic independence of the values of Mahler functions in a certain case of positive characteristic

AKINARI GOTO, TAKA-AKI TANAKA

Diophantine Analysis and Related Fields 2015 6 Mar 2015 Gunma University