Preface

学生向けの情報

専門分野: 差分代数
どんな研究? 倍角公式をもつ関数を公式の形に注目して分類しています。

卒研ページに卒研で使った本のリストがあります。

Research interests

quadrature and reduction of algebraic difference/differential equations, difference/differential algebra, discrete/continuous Painlevé equations.

Articles

Preprints

  1. Nishioka, S., Transcendence of solutions of q-Airy equation.

Accepted

  1. Nishioka, S., Irreducibility of discrete Painlevé equation of type $D_7^{(1)}$, To appear in Funkcialaj Ekvacioj.
  2. Nishioka, S., Proof of unsolvability of q-Bessel equation using valuations. To appear in Journal of Mathematical Sciences the University of Tokyo

Published

  1. Nishioka, K., Nishioka, S., Autonomous equations of Mahler type and transcendence, Tsukuba Journal of Mathematics, Vol. 39, No. 2 (2015), 251--257.
  2. Nishioka, S., Functions satisfying Poincaré's multiplication formula, Osaka Journal of Mathematics, 51 (2014), 141--160.
  3. Nakazono, N., Nishioka, S., Solutions to a q-analog of Painlevé III equation of type $D_7^{(1)}$. Funkcialaj Ekvacioj, 56 (2013), 415--439.
  4. Nishioka, S., Approximation of Poincaré's new functions by rational functions, Journal of Difference Equations and Applications, Volume 19, Issue 9 (2013), 1452--1462.
    doi:10.1080/10236198.2012.755963
    (Available online: 2013-02-06)
  5. Nishioka, S., Algebraic independence of solutions of first-order rational difference equations, Results in Mathematics, Volume 64, Issue 3 (2013), 423--433.
    doi:10.1007/s00025-013-0324-8
  6. Nishioka, S., Non-elementary solutions of difference equations, J. Differ. Equ. Appl., Volume 19, Issue 1 (2013), 54--58.
    doi:10.1080/10236198.2011.618498
  7. Nishioka, K., Nishioka, S., Algebraic theory of difference equations and Mahler functions, Aequationes Mathematicae, Volume 84, Issue 3 (2012), 245--259.
    doi:10.1007/s00010-012-0132-3
  8. Nishioka, S., Irreducibility of $q$-Painlevé equation of type $A_6^{(1)}$ in the sense of order, J. Differ. Equ. Appl., Volume 18, Issue 2 (2012), 313--333.
    doi:10.1080/10236198.2010.491824
  9. Nishioka, S., Transcendence of solutions of $q$-Painlevé equation of type $A_6^{(1)}$, Aequat. Math., 81 (2011), 121--134.
    doi:10.1007/s00010-010-0054-x
  10. Nishioka, S., Decomposable extensions of difference fields, Funkcial. Ekvac., 53 (2010), 489--501.
  11. Nishioka, S., Solvability of Difference Riccati Equations by Elementary Operations, J. Math. Sci. Univ. Tokyo, 17 (2010), 159--178.
  12. Nishioka, S., Transcendence of Solutions of $q$-Painlevé Equation of Type $A_7^{(1)}$, Aequat. Math., 79 (2010), 1--12.
    doi:10.1007/s00010-010-0007-4
  13. Nishioka, S., On Solutions of $q$-Painlevé Equation of Type $A_7^{(1)}$, Funkcial. Ekvac., 52 (2009), 41--51.
  14. Nishioka, S., Difference algebra associated to the $q$-Painlevé equation of type $A_7^{(1)}$, RIMS Kôkyûroku Bessatsu, Vol. B10 (2008), 167--176.

Proceedings

  1. 西岡斉治, 差分Riccati方程式の可解性, 数理解析研究所講究録1765「可積分系数理の多様性」 (2011), 64--71.

Lectures

International conferences

2015-10-19/23 Differential and Difference Equations: Analytic, Arithmetic and Galoisian Approaches, Lille (Laboratoire Paul Painlevé), France
[en] 「Double-angle formulae and algebraic independence」, 2015-10-20
2015-04-07/10 Model Theory, Difference/Differential Equations and Applications, CIRM, France
[en] 「Double-Angle Formulae and Algebraic Independence」, 2015-04-08
2014-11-17/21 Recent developments in differential equations in the complex domain, RIMS, Kyoto University, Japan
[en] 「Reducibility of algebraic difference equations」, 2014-11-18
2012-07-11 Nonlinear Evolution Equations and Dynamical Systems 2012, Orthodox Academy of Crete, Greece
[en] Nobutaka, N. (presenter), Nishioka, S., Study on a q-analog of the Painleve III equation of type D_7^{(1)}
2012-06-10/16 SIDE10 International Conference, 中華人民共和国(浙江省寧波市)・Yin Feng Holiday Resort
[en] Nakazono, N. (presenter), Nishioka, S., Study on a q-analog of the Painleve III equation of type D7, 2012-06-15
2012-01-04/07 Joint Mathematics Meetings, Boston, USA, AMS Special Session on Differential Algebraic Geometry and Galois Theory (in memory of Jerald Kovacic), 2012-01-05/06.
[en] Solvability of difference Riccati equations, 2012-01-05.
2010-06-24/25 Equations différentielles, équations fonctionnelles, Université d'Angers, France
[en] Irreducibility of q-Painlevé equation, 2010-06-25
2009-05-11/15 Algebraic Theory of Difference Equations, University of Leeds, UK
[en] Irreducibility of q-Painlevé equation of type $A_6^{(1)}$ in the sense of order, 2009-05-13.
2007-10-11 Differential Equations and Exact WKB Analysis, Research Institute for Mathematical Sciences, Kyoto University
[en, ja] Difference algebra associated to the $q$-Painlevé equation of type $A_7^{(1)}$

by poster

2016-07-03/09 SIDE 12, Quebec, Canada
[en] 「Irreducibility of difference Painleve equations」
2011-07-25/29 Infinite Analysis 11 ~ Frontier of Integrability ~, The University of Tokyo, Japan
[en] Approximation of solutions of Poincaré's multiplication formulas by rational functions, poster, 2011-07-27.
2008-06-09/13 From Painlevé to Okamoto, The University of Tokyo, Japan
[en] General Investigation On Decomposable Extension, poster, 2008-06-10/12

Domestic conferences

2016-11-26/27 表現論と微分方程式, 城西大学, 東京都
[ja] 「反復差分リッカチ方程式の解の超越性」, 2016-11-27
2014-08-05/08 2014函数方程式論サマーセミナー, KKR伊豆長岡保養所「千歳荘」, 静岡県
[ja] 「超越古典関数がないこと(既約性)」, 2014-08-05
2013-09-14/15 Workshop on Galois point and related topics, 山形大学理学部
[ja] 差分代数と超越数論, 2013-09-15
2013-08-06/09 2013函数方程式論サマーセミナー, リゾートホテル阿蘇いこいの村, 熊本県
[ja] 倍角公式と代数的独立性, 2013-08-09
2013-01-26/28 ウィンターセミナー2013, KKR湯沢ゆきぐに, 新潟県
[ja] 差分リッカチ方程式の標準型, 2013-01-28
2012-09-18 日本数学会2012年度秋季総合分科会, 九州大学, 福岡県
[ja] Poincaréの新しい関数の有理関数による近似
2012-09-14/17 力学系勉強会, 九州大学九重共同研修所, 大分県
[ja] Picard-Vessiot理論(I)~(IV), 差分方程式と可解性
2012-08-07/10 2012函数方程式論サマーセミナー, 蔵王白銀荘, 山形市
[ja] q-P^{D_7^{(1)}}_{III}の代数関数解(II), 2012-08-10
2010-11-15/17 非線形数理若手の会(勉強会), 九州大学西新プラザ, 福岡市
[ja] 差分方程式の非初等的解, 2010-11-16
2010-08-18/20 RIMS研究集会2010「可積分系数理の多様性」 - Diversity of the Theory of Integrable Systems -, 京都大学
[ja] 差分Riccati方程式の可解性, 2010-08-19
2010-03-24/27 日本数学会2010年度年会, 慶應義塾大学
[ja] 中園信孝 (presenter), 西岡斉治, $\tilde{W}(A_4^{(1)})$から得られる $q$パンルヴェ方程式, 2010-03-27
2009-11-19/21 研究集会「非線形波動研究の現状と将来」, 応用力学研究所
[ja] 中園信孝 (presenter), 西岡斉治, $A_4$型アフィンワイル群対称性を持つ$q$-パンルヴェ方程式, 2009-11-20
2009-07-21/24 玉原特殊多様体研究集会, 玉原国際セミナーハウス
[ja] q-Bessel の非可解性, 2009-07-23.
2009-03-26/29 日本数学会2009年度年会(東京大学)
[ja] $q$-Painlevé II の irreducibility, 2009-03-28.
2007-09-21 日本数学会2007年度総合分科会 無限可積分系セッション(東北大学)
[ja] $A_7$型$q$-差分Painlevé方程式の解の超越性

Seminars

France

2013-02-12 Séminaire Equations fonctionnelles, Université de Strasbourg, France
[en] Approximation of Poincare's new functions by rational functions
2010-06-29 Séminaire Equations fonctionnelles, Université de Strasbourg, France
[en] Irreducibility of q-Painlevé equation

Japan

2015-11-06 広島複素解析セミナー, 広島大学
[ja] 「倍角公式と代数的独立性」
2012-12-12/13 つくば微分ガロア理論セミナー, 筑波大学
[ja] 差分方程式から見た関数の初等性, 2012-12-13
2012-07-11 古典解析セミナー, 東京大学
[ja] 中園信孝, 西岡斉治 (presenter), On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions
2011-05-27 物理・数理コロキウム, 青山学院大学
[ja] 差分方程式の非可解性の簡易判定法
2011-05-18 古典解析セミナー, 大阪大学
[ja] 乗法公式を持つベキ級数の有理関数による近似
2011-02-16/18 古典解析セミナー・ミニ研究集会, The University of Tokyo, Japan
[en] Solvability of difference Riccati equations, 2011-02-16
2010-01-20 古典解析セミナー, 大阪大学
[ja] A_6^{(1)}型q-Painlevé方程式の解の超越性
2010-01-12 Lie群論・表現論セミナー, 東大
[ja] 代数的差分方程式の可解性と既約性
2008-12-06 古典解析セミナー(阪大)
[ja] q-Painlevé II の irreducibility
2007-05-30 古典解析セミナー(阪大)
[ja] $A_7$型$q$-パンルヴェ方程式の解の超越性と$A_6$型について
2007-01-19 九州可積分系セミナー(九州大学)
[ja] $q$-$P(A_7^{(1)})$の解の超越性