Research Output per year

## Fingerprint Dive into the research topics where Takaaki Tanaka is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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Algebraic Independence
Mathematics

Linear Recurrence
Mathematics

Algebraic number
Mathematics

Infinite product
Mathematics

Lame number
Mathematics

Transcendence
Mathematics

Independence Results
Mathematics

Power series
Mathematics

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## Research Output 1996 2018

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

Tanaka, T. & Tanuma, Y., 2018 Jun 26, (Accepted/In press) In : International Journal of Number Theory. p. 1-16 16 p.Research output: Contribution to journal › Article

Algebraic Independence

Algebraic number

Derivative

Series

Irrational number

## 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, A. & Tanaka, T., 2017, (Accepted/In press) In : Journal of Number Theory.Research output: Contribution to journal › Article

Algebraic Independence

Relatively prime

Positive Characteristic

Functional equation

Algebraic number

## Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers

Kaneko, H., Tachiya, Y., Kurosawa, T. & Tanaka, T., 2015, In : Acta Arithmetica. 168, 2, p. 161-186 26 p.Research output: Contribution to journal › Article

Lucas numbers

Infinite product

Lame number

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

Kurosawa, T., Tachiya, Y. & Tanaka, T., 2014, In : Monatshefte fur Mathematik. 174, 1, p. 77-104 28 p.Research output: Contribution to journal › Article

Independence Results

Algebraic Independence

Infinite product

Linear Recurrence

Entire Function

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

Tanaka, T., 2014 Jun 1, In : Tokyo Journal of Mathematics. 37, 1, p. 211-223 13 p.Research output: Contribution to journal › Article

Functional equation

Algebraic Independence

Independence Results

Several Variables

Linear Combination