原著論文（査読付き）

• T. Tanaka and Y. Tanuma: Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers, Int. J. Number Theory 14 (2018), 2369-2384.
• A. Goto and T. Tanaka: 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, J. Number Theory 184 (2018), 384-410.
• H. Kaneko, T. Kurosawa, Y. Tachiya, and T. Tanaka: Explicite algebraic dependence formulae of infinite products related with Fibonacci and Lucas numbers, Acta Arith. 168 (2015), 161-186.
• T. Kurosawa, Y. Tachiya, and T. Tanaka: Algebraic independence results for the values of certain Mahler functions and their application to infinite products, Monatsh. Math. 174 (2014), 77-104.
• T. Tanaka: Arithmetic properties of solutions of certain functional equations with transformations represented by matrices including a negative entry, Tokyo J. Math. 37 (2014), 211-223.
• T. Kurosawa, Y. Tachiya, and T. Tanaka: Algebraic relations with the infinite products generated by Fibonacci numbers, Ann. Math. Inform. 41 (2013), 107-119.
• T. Kurosawa, Y. Tachiya, and T. Tanaka: Algebraic independence of infinite products generated by Fibonacci numbers, Tsukuba J. Math. 34 (2010), 255-264.
• T. Tanaka: Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences, J. Number Theory 129 (2009), 3081-3093.
• T. Tanaka: Algebraic independence of modified reciprocal sums of products of Fibonacci numbers, Tsukuba J. Math. 30 (2006), 345-361.
• T. Tanaka: Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences, Osaka J. Math. 42 (2005), 487-497.
• T. Tanaka: Algebraic independence of power series generated by linearly independent positive numbers, Results Math. 46 (2004), 367-380.
• T. Tanaka: Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion, J. Number Theory 105 (2004), 38-48.
• T. Tanaka: Algebraic independence of Fibonacci reciprocal sums associated with Newton’s method, Tsukuba J. Math. 27 (2003), 375-387.
• D. Duverney, T. Kanoko, and T. Tanaka: Transcendence of certain reciprocal sums of linear recurrences, Monatsh. Math. 137 (2002), 115-128.
• T. Tanaka: Transcendence of the values of certain series with Hadamard’s gaps, Arch. Math. 78 (2002), 202-209.
• K. Nishioka, T. Tanaka, and Z.-Y. Wen: Substitution in two symbols and transcendence, Tokyo J. Math. 22 (1999), 127-136.
• T. Tanaka: Algebraic independence results related to linear recurrences, Osaka J. Math. 36 (1999), 203-227.
• K. Nishioka, T. Tanaka, and T. Toshimitsu: Algebraic independence of sums of reciprocals of the Fibonacci numbers, Math. Nachr. 202 (1999), 97-108.
• T. Tanaka: Algebraic independence of the values of power series generated by linear recurrences, Acta Arith. 74 (1996), 177-190.
• T. Tanaka: Algebraic independence of certain numbers defined by linear recurrences, Keio Sci. Tech. Reports 47 (1994), 11-20.

 　その他の主要論文（査読なし）

• 田中 孝明: Algebraic independence of the values of a certain map defined on the set of orbits of the action of Klein four-group, 数理解析研究所講究録2131　解析的整数論とその周辺, 京都大学数理解析研究所, 2019年, pp. 177-187.
• 黒沢 健, 立谷 洋平, 田中 孝明: Algebraic independence of the values of certain infinite products and their derivatives related to Fibonacci and Lucas numbers, 数理解析研究所講究録1874　解析的整数論とその周辺 ー近似と漸近的手法を通して見た数論, 京都大学数理解析研究所, 2014年, pp. 81-93.
• T. Tanaka: Algebraic independence properties related to certain infinite products, AIP Conference Proceedings 1385　Diophantine Analysis and Related Fields 2011, American Institute of Physics, 2012, pp. 116-123.
• 田中孝明: Algebraic independence of certain series involving continued fractions and generated by linear recurrences, 数理解析研究所講究録1639　解析的整数論の新しい展開（New Aspects of Analytic Number Theory）, 京都大学数理解析研究所, 2009年, pp. 36-49.
• T. Tanaka: Algebraic independence of a certain series and its subseries with subscripts in a geometric progression, Seminar on Math. Sci. No. 35 　Diophantine Analysis and Related Fields 2006, Keio Univ., 2006, pp. 175-185.
• T. Tanaka: Algebraic independence of functions satisfying certain Mahler type functional equations and its applications, Colloque Franco.Japonais Th´eorie des nombres transcendants 日仏超越数論研究集会報告集, Seminar on Math. Sci. No. 27, Keio Univ., 1999, pp. 21-49.

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