Global study of nonlinear special functions and its application

• Project/Area Number: 22340037
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Keio University
• Principal Investigator: SHIMOMURA Shun 慶應義塾大学, 理工学部, 教授 (00154328)
• Co-Investigator(Kenkyū-buntansha): SHIOKAWA Iekata 慶應義塾大学, 理工学部, 名誉教授 (00015835) ; TANI Atusi 慶應義塾大学, 理工学部, 名誉教授 (90118969)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2010: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: Painleve方程式 / 漸近表現 / 差分Painleve方程式 / Riemann zeta-function / 4乗平均 / Ramanujan q-series / ドイツ:アメリカ / 国際研究者交流 / Riemann zeta 関数 / ４乗平均 / ロシア / 値分布 / Fibonacci数 / 代数的独立性 / 楕円関数 / Eisenstein級数 / 亀裂先端伝播 / 反平面(mod 3)モデル方程式 / kinked crack

Research Abstract

For truncated solutions of the Painleve equation (V), we estimated the frequency of a-points including poles outside their proper sectors. For the difference Painleve equation (dII) we obtained asymptotic expressions of certain solutions describing how th

Research Products

• [Journal Article] Fourth moment of the Riemann zeta-function with a shift along the real line (2013)
  • Author(s): Shimomura, Shun
  • Journal Title: Tokyo J. Math. Volume: to appear
• [Journal Article] Frequency of a-points for the fifth and the third Painleve transcendents in a sector (2013)
  • Author(s): Shimomura, Shun
  • Journal Title: Tohoku Math. J. Volume: to appear
• [Journal Article] Algebraic independence of certain numbers related to modular functions (2012)
  • Author(s): Carsten Elsner, Shun Shimomura and Iekata Shiokawa
  • Journal Title: Functiones et Approximatio Commentarii Mathematici Volume: 47 Pages: 121-141
  • Peer Reviewed
• [Journal Article] Shifted fourth moment of the Riemann zeta-function (2012)
  • Author(s): Shun Shimomura
  • Journal Title: Acta Math. Hungarica Volume: 137 Pages: 104-129
  • Peer Reviewed
• [Journal Article] Rational solutions of difference Painleve equations (2012)
  • Author(s): Shun Shimomura
  • Journal Title: Tokyo J. Math Volume: 35 Pages: 85-95
  • Peer Reviewed
• [Journal Article] Continuous limit of the difference second Painleve equation and its asymptotic solutions (2012)
  • Author(s): Shun Shimomura
  • Journal Title: J. Math. Soc. Japan Volume: 64 Pages: 733-781
  • Peer Reviewed
• [Journal Article] Asymptoticbehaviour at a tip of a rigid line inclusion in linearized elasticity (2012)
  • Author(s): Hiromichi Itou, A. M. Khludnev, E. M. Rudoy and Atusi Tani
  • Journal Title: ZAMM Z. Angew. Math. Mech Volume: 92 Pages: 716-730
  • Peer Reviewed
• [Journal Article] Small-time existence of a strong solution of primitive equations for the ocean (2012)
  • Author(s): Hirotada Honda and Atusi Tani
  • Journal Title: Tokyo J. Math. Volume: 35 Pages: 97-138
  • Peer Reviewed
• [Journal Article] Rational solutions of difference Painleve equations (2012)
  • Author(s): Shimomura, Shun
  • Journal Title: Tokyo J. Math. Volume: 35 Pages: 85-95
  • Peer Reviewed
• [Journal Article] Shifted fourth moment of the Riemann zeta-function (2012)
  • Author(s): Shimomura, Shun
  • Journal Title: Acta Math. Hungar. Volume: 137 Issue: 1-2 Pages: 104-129
  • DOI: 10.1007/s10474-012-0203-x
  • Peer Reviewed
• [Journal Article] Algebraic relations for reciprocal sums of even terms of a Fibonacci sequence (2012)
  • Author(s): Elsner, Shimomura, Shiokawa
  • Journal Title: J.Math.Sci.(N.Y.) Volume: 180 Pages: 650-671
  • Peer Reviewed
• [Journal Article] Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers,Diophantine Analysis and Related Fields DARF 2011, AIP Conference Proceedings 1385 (2011)
  • Author(s): Carsten Elsner, Shun Shimomura and Iekata Shiokawa
  • Journal Title: American Institute of Physics, Melville, New York Pages: 17-31
• [Journal Article] Truncated solutions of the fifth Painleve equation (2011)
  • Author(s): Shun Shimomura
  • Journal Title: Funkcial. Ekvac Volume: 54 Pages: 451-471
  • Peer Reviewed
• [Journal Article] Algebraic independence results for reciprocal sums of Fibonacci numbers (2011)
  • Author(s): Carsten Elsner, Shun Shimomura and Iekata Shiokawa
  • Journal Title: Acta Arithmetica Volume: 148 Pages: 205-223
  • Peer Reviewed
• [Journal Article] Nonlinear waves in incompressible viscoelastic Maxwell medium (2011)
  • Author(s): V. Yu. Liapidevskii, V. V. Pukhnachevand Atusi Tani
  • Journal Title: Wave Motion Volume: 48 Pages: 727-737
  • Peer Reviewed
• [Journal Article] On the Hasegawa-Wakatani equations with vanishing resistivity. (2011)
  • Author(s): Shintaro Kondo and Atusi Tani
  • Journal Title: Proc. Japan Acad. Ser. A Math. Sci. Volume: 87 Pages: 156-161
  • NAID: 40019128058
  • Peer Reviewed
• [Journal Article] Initial boundary value problem of Hasegawa - Wakatani equations with vanishing resistivity. (2011)
  • Author(s): Shintaro Kondo and Atusi Tani
  • Journal Title: Adv. Math. Sci. Appl Volume: 21 Pages: 223-253
  • Peer Reviewed
• [Journal Article] Truncated solutions of the fifth Painleve equation (2011)
  • Author(s): Shun Shimomura
  • Journal Title: Funkcial.Ekvac. Volume: 54 Pages: 451-471
  • Peer Reviewed
• [Journal Article] Algebraic independence results for reciprocal sums of Fibonacci numbers (2011)
  • Author(s): Elsner, Shimomura, Shiokawa
  • Journal Title: Acta Arith. Volume: 148 Pages: 205-223
  • Peer Reviewed
• [Journal Article] Algebraic relations for reciprocal sums of even terms in Fibonacci numbers (Russian) (2010)
  • Author(s): Carsten Elsner, Shun Shimomura and Iekata Shiokawa
  • Journal Title: Fundam.Prikl. Mat. Volume: 16 Pages: 173-200
  • Peer Reviewed
• [Journal Article] Algebraic independence results for the sixteen families of q-series (2010)
  • Author(s): Carsten Elsner, Shun Shimomura and Iekata Shiokawa and Yohei Tachiya
  • Journal Title: Ramanujan J Volume: 22 Pages: 315-344
  • Peer Reviewed
• [Journal Article] Modularity gap for Eisenstein series (2010)
  • Author(s): Shun Shimomura
  • Journal Title: Proc. Japan Acad. Ser. A Volume: 86 Pages: 79-84
  • Peer Reviewed
• [Journal Article] A remark on Nesterenko's theorem for Ramanujan functions (2010)
  • Author(s): Carsten Elsner, Shun Shimomura and Iekata Shiokawa
  • Journal Title: Ramanujan J Volume: 21 Pages: 211-221
  • Peer Reviewed
• [Journal Article] Modularity gap for Eisenstein series (2010)
  • Author(s): Shun Shimomura
  • Journal Title: Proc.Japan Acad.Ser.A Math.Sci. Volume: 86 Pages: 79-84
  • Peer Reviewed
• [Journal Article] A remark on Nesterenko's theorem for Ramanujan functions (2010)
  • Author(s): E.Carsten, S.Shimomura, I.Shiokawa
  • Journal Title: Ramanujan J. Volume: 21 Pages: 211-221
  • Peer Reviewed
• [Journal Article] On the topological derivative due to kink of a crack with non-penetration (2010)
  • Author(s): A.M.Khludnev, V.A.Kovtunenko, A.Tani
  • Journal Title: J.Math.Pures Appl. Volume: 94 Pages: 571-596
  • Peer Reviewed
• [Journal Article] Frequency of a-points for the fifth and the third Painleve transcendents in a sector
  • Author(s): Shun Shimomura
  • Journal Title: Tohoku Math. J
  • Peer Reviewed
• [Journal Article] Fourth moment of the Riemann zeta-function with a shift along the real line
  • Author(s): Shun Shimomura
  • Journal Title: Tokyo J. Math
  • Peer Reviewed
• [Presentation] Algebraic independence results for the sixteen families of q-series (2010)
  • Author(s): 塩川宇賢
  • Organizer: 数理解析研究所研究集会Analytic Number Theory
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-10-04