Papers - Shimomura, Shun

On a General Singular Solution of the Fifth Painlevé Equation Along the Positive Real Axis

Shimomura S.

Computational Methods and Function Theory (Computational Methods and Function Theory)   2021

ISSN  16179447

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We propose a system of non-linear equations equivalent to the fifth Painlevé equation, which enables us to examine the general singular solution given by Andreev and Kitaev along the positive real axis. We present a two-parameter family of asymptotic solutions corresponding to this general singular solution, and pose a conjecture.

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Elliptic asymptotic representation of the fifth Painleve transcendents

Shun Shimomura

(arXiv:2012.07321, math.CA, math-ph, 54 pages)   2020.12

Research paper (other academic), Single Work

Three-parameter solutions of the PV Schlesinger-type equation near the point at infinity and the monodromy data

Shimomura S.

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) (Symmetry, Integrability and Geometry: Methods and Applications (SIGMA))  14 2018

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© 2018, Institute of Mathematics. All rights reserved. For the Schlesinger-type equation related to the fifth Painlevé equation (V) via isomonodromy deformation, we present a three-parameter family of matrix solutions along the imaginary axis near the point at infinity, and also the corresponding monodromy data. Two-parameter solutions of (V) with their monodromy data immediately follow from our results. Under certain conditions, these solutions of (V) admit sequences of zeros and of poles along the imaginary axis. The monodromy data are obtained by matching techniques for a perturbed linear system.

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Critical behaviours of the fifth Painleve transcendents and the monodromy data

SHIMOMURA SHUN

Kyushu J. Math. 71   139 - 185 2017

Research paper (bulletin of university, research institution), Single Work, Accepted

Logarithmic solutions of the fifth Painleve equation near the origin

SHIMOMURA SHUN

Tokyo J. Math. 39 ( 3 ) 797 - 825 2017

Research paper (scientific journal), Single Work, Accepted

Series expansions of Painleve transcendents near the point at infinity

SHIMOMURA SHUN

Funkcial. Ekvac. 58   277 - 319 2015

Research paper (scientific journal), Single Work, Accepted

The sixth Painleve transcendents and the associated Schlesinger equation

SHIMOMURA SHUN

Publ. RIMS Kyoto Univ. 51   417 - 463 2015

Research paper (scientific journal), Single Work, Accepted

• Access to Document (DOI)

Fourth moment of the Riemann zeta-function with a shift along the real line

SHIMOMURA SHUN

Tokyo J. Math. 36   355 - 377 2013

Research paper (scientific journal), Single Work, Accepted

Frequency of a-points for the fifth and the third Painleve transcendents in a sector

SHIMOMURA SHUN

Tohoku Math. J. 65   591 - 605 2013

Research paper (scientific journal), Single Work, Accepted

Shifted fourth moment of the Riemann zeta-function

SHIMOMURA SHUN

Acta Math. Hungar. 137 ( 1-2 ) 104–129 2012

Research paper (scientific journal), Single Work, Accepted

Continuous limit of the difference second Painlevé equation and its asymptotic solutions

SHIMOMURA SHUN

J. Math. Soc. Japan 64 ( 3 ) 733–781 2012

Research paper (scientific journal), Single Work, Accepted

Rational solutions of difference Painlevé equations

SHIMOMURA SHUN

Tokyo J. Math 35 ( 1 ) 85–95 2012

Research paper (scientific journal), Single Work, Accepted

Algebraic independence of certain numbers related to modular functions

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Funct. Approx. Comment. Math. 47 ( 1 ) 121–141 2012

Research paper (scientific journal), Joint Work, Accepted

Truncated solutions of the fifth Painleve equation

SHIMOMURA SHUN

Funkcial. Ekvac. 54   451--471 2011

Research paper (scientific journal), Single Work, Accepted

Algebraic independence results for reciprocal sums of Fibonacci numbers

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Acta Arith. 148 ( 3 ) 205–223 2011

Research paper (scientific journal), Joint Work, Accepted

Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Diophantine Analysis and Related Fields DARF 2011, AIP Conference Proceedings 1385, American Institute of Physics (Melville, New York)  1385   17-31 2011

Research paper (scientific journal), Joint Work

Algebraic relations for reciprocal sums of even terms of a Fibonacci sequence. (Russian)

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Fundam. Prikl. Mat. ; English translation in J. Math. Sci. (N. Y.) 180 (2012), no. 5, 650–671 16 ( 5 ) 173--200 2010

Research paper (scientific journal), Joint Work, Accepted

A remark on Nesterenko's theorem for Ramanujan functions

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Ramanujan J. 21   211--221 2010

Research paper (scientific journal), Joint Work, Accepted

Modularity gap for Eisenstein series

SHIMOMURA SHUN

Proc. Japan Acad. Ser. A 86   79--84 2010

Research paper (scientific journal), Single Work, Accepted

Algebraic independence results for the sixteen families of q-series

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata; Tachiya, Yohei

Ramanujan J. 22 ( 3 ) 315–344 2010

Research paper (scientific journal), Joint Work, Accepted

Asymptotic representations for Fibonacci reciprocal sums and Euler's formula for zeta values

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

J. Theor. Nombres Bordeaux 21   145--157 2009

Research paper (scientific journal), Joint Work, Accepted

Some estimates for logarithmic derivatives of meromorphic functions

SHIMOMURA SHUN

Result. Math. 54   173--182 2009

Research paper (scientific journal), Single Work, Accepted

Meromorphic solutions of difference Painlev'e equations

SHIMOMURA SHUN

J. Phys. A: Math. Theor. 42   315213 (19pp) 2009

Research paper (scientific journal), Single Work, Accepted

Nonlinear differential equations of second Painlev'e type with the quasi-Painlev'e property

SHIMOMURA SHUN

Tohoku Math. J. 60   581--595 2008

Research paper (scientific journal), Single Work, Accepted

Reciprocal sums of Fibonacci numbers

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Diophantine Analysis and Related Fields DARF 2007/2008, AIP Conference Proceedings 976, American Institute of Physics (Melville, New York)  976   77--89 2008

Research paper (scientific journal), Joint Work

Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Ramanujan J. 17   429--446 2008

Research paper (scientific journal), Joint Work, Accepted

Equi-distribution of values for the third and the fifth Painlev'e transcendents

SHIMOMURA SHUN

Nagoya Math. J. 192   89--109 2008

Research paper (scientific journal), Single Work, Accepted

Algebraic relations for reciprocal sums of Fibonacci numbers

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Acta Arith. 130   37--60 2007

Research paper (scientific journal), Joint Work, Accepted

A class of differential equations of PI-type with the quasi-Painlev'e property

SHIMOMURA SHUN

Ann. Mat. Pura Appl. 186   267--280 2007

Research paper (scientific journal), Single Work, Accepted

Asymptotic solutions of a degenerate Garnier system of the first Painlev'e type

SHIMOMURA SHUN

RIMS K^{o}ky^{u}roku Bessatsu B2   227--237 2007

Research paper (scientific journal), Single Work, Accepted

Algebraic relations for reciprocal sums of binary recurrences

Elsner, Carsten; SHIMOMURA SHUN; Shiokawa, Iekata

Diophantine Analysis and Related Fields 2006, In honor of Iekata Shiokawa, Seminar on Mathematical Sciences, Keio University (Keio University)  35   77--92 2006

Research paper (scientific journal), Joint Work

A family of solutions of a higher-ordre PVI equation near a regular singularity

SHIMOMURA SHUN

J. Phys. A: Math. Gen. 39   12153--12165 2006

Research paper (scientific journal), Single Work, Accepted

Meromorphic solutions of Riccati differential equations with doubly periodic coefficients

SHIMOMURA SHUN

J. Math. Anal. Appl. 304   644--651 2005

Research paper (scientific journal), Single Work, Accepted

On certain nonlinear differential equations

SHIMOMURA SHUN

Proceedings of the 12th International Conference on Finite or Infinite Dimentional Complex Analysis and Applications, (Kyushu University Press)     299--304 2005

Research paper (scientific journal), Single Work

Growth of modified Painleve transcendents of the fifth and the third kind

SHIMOMURA SHUN

Forum Math. 16 ( x ) 231-247 2004

Research paper (scientific journal), Single Work, Accepted

Lower estimates for the growth of the fourth and the second Painleve transcendents

SHIMOMURA SHUN

Proc. Edinburgh Math. Soc. 47 ( x ) 231-249 2004

Research paper (scientific journal), Single Work, Accepted

Poles and alpha-points of meromorphic solutions of the first Painleve hierarchy

SHIMOMURA SHUN

Publ. Res. Inst. Math. Sci. 40 ( 2 ) 471-485 2004

Research paper (scientific journal), Single Work, Accepted

On the number of poles of the first Painleve transcendents and higher order analogues

SHIMOMURA SHUN

Symposium on Complex Differential and Functional Equations, University of Joensuu, Department of Mathematics, Report Series 6 ( x ) 149-154 2004

Research paper (scientific journal), Single Work, Accepted

A certain expression of the first Painleve hierarchy

SHIMOMURA SHUN

Proc. Japan Acad. Ser. A 80 ( 6 ) 105-109 2004

Research paper (scientific journal), Single Work, Accepted

On second order nonlinear differential equations with the quasi-Painleve property

SHIMOMURA SHUN

数理解析研究所講究録 1367 x ( x ) 204-210 2004

Research paper (scientific journal), Single Work

Growth of the first, the second and the fourth Painlev'e transcendents

SHIMOMURA SHUN

Math. Proc. Camb. Phil. Soc. 134   259-269 2003

Research paper (scientific journal), Single Work, Accepted

Riccati differential equations with elliptic coefficients,Ⅱ

Ishizaki,Katsuya; Laine, Ilpo; SHIMOMURA SHUN; Tohge, Kazuya

Tohoku Math. J. 55   99-108 2003

Research paper (scientific journal), Joint Work, Accepted

Meromorphic solutions of Painlev'e differential equations

SHIMOMURA SHUN

Complex Differential and Functional Equations, Mekrij\"arvi 2000, ed. by I. Laine, University of Joensuu, Department of Mathematics, Report Series 5 ( x ) 107-124 2003

Research paper (scientific journal), Single Work, Accepted

Proofs of the Painleve property for all Painleve equations

SHIMOMURA SHUN

Japan. J. Math. 29 ( 2 ) 159-180 2003

Research paper (scientific journal), Single Work, Accepted

Loweer estimates for the growth of Painleve transcendents

SHIMOMURA SHUN

Funkcial. Ekvac. 46 ( 2 ) 287-295 2003

Research paper (scientific journal), Single Work, Accepted

On the number of poles of the first Painleve transcendents and higher order analogues II

SHIMOMURA SHUN

数理解析研究所講究録 1316 x ( x ) 13-18 2003

Research paper (scientific journal), Single Work

On deficiencies of small functions for Painlev'e transcendents of the fourth kind

SHIMOMURA SHUN

Ann. Acad. Sci. Fenn. Ser. A I Math. 27   109-120 2002.03

Research paper (scientific journal), Single Work, Accepted

Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients

SHIMOMURA SHUN

Nagoya Math. J. 166   55-82 2002

Research paper (scientific journal), Single Work, Accepted

Nevanlinna theory and Painlev'e transcendents

下村 俊

数理解析研究所講究録　1280    85-97 2002

Single Work

On the number of poles of the first Painlev'e transcendents and higher order analogues

下村 俊

数理解析研究所講究録　1296    124-127 2002

Single Work

On the Painlev'e I hierarchy

数理解析研究所講究録 1203    46-50 2001.04

Pole loci of solutions of a degenerate Garnier system

SHIMOMURA SHUN

Nonlinearity 14   193--203 2001.03

Research paper (scientific journal), Single Work, Accepted

The first, the second and the fourth Painlev'e transcendents are of finite order

SHIMOMURA SHUN

Proc. Japan Acad. Ser. A vol 77   42--45 2001.03

Research paper (scientific journal), Single Work, Accepted

Painlev'e property of a degenerate Garnier system of (9/2)-typeand of a certain fourth order non-linear ordinary differential equation

SHIMOMURA SHUN

Ann. Scuola Norm. Sup. Pisa vol 29   1-17 2000

Research paper (scientific journal), Single Work, Accepted

Riccati differential equations with elliptic coefficients

Ishizaki, Katsuya; Laine, Ilpo; SHIMOMURA SHUN; Tohge, Kazuya

Result. Math. 38   58--71 2000

Research paper (scientific journal), Joint Work, Accepted

On meromorphic solutions of a linear differential equation with doubly periodic coefficients

SHIMOMURA SHUN

Illinois J. Math. 44   593--601 2000

Research paper (scientific journal), Single Work, Accepted

Value distribution of Painlev'e transcendents of the first and the second kind

SHIMOMURA SHUN

J. Anal. Math. 82   333--346 2000

Research paper (scientific journal), Single Work, Accepted

Value distribution of Painlev'e transcendents of the fifth kind

SHIMOMURA SHUN

Result. Math. 38   348--361 2000

Research paper (scientific journal), Single Work, Accepted

On deficiencies and ramification indices for Painlev'e transcendents of the second kind

SHIMOMURA SHUN

Proceedings of the Second ISAAC CongressVol 1, Kluwer, Dordrecht    489--493 2000

Research paper (conference, symposium, etc.), Single Work

退化 Garnier 系の解の極集合について

数理解析研究所講究録 1133    68--71 2000

Single Work

ある退化 Garnier 系と ４階 Painlev'e 方程式

-- パンルヴェ方程式の眺望 -- Rokko Lectures in Mathematics（神戸大学）7,    41 - 47 2000

Single Work

A confluent hypergeometric system associated with Phi_3 and a confluent Jordan-Pochhammer equation

SHIMOMURA SHUN

Fukcial. Ekvac. 42   225-240 1999.08

Research paper (scientific journal), Single Work, Accepted

Value distribution of Painlev'e transcendents of the third kind

SHIMMURA SHUN

Complex Variables 40   51-62 1999

Research paper (scientific journal), Single Work, Accepted

On a generalized Bessel function of two variables II.Case of coalescing saddle points

SHIMOMURA SHUN

Tohoku Math. J. 50   389-406 1998.09

Research paper (scientific journal), Single Work, Accepted

Asymptotic expansions and Stokes multipliers of the confluent hyper geometric function　Φ２　Ⅱ Behavior near（∞，∞）in P1(σ)×P1(σ)

SHIMOMURA SHUN

J.Math. Soc. Japan 50   1--22 1998.01

Research paper (scientific journal), Single Work, Accepted

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Φ２のみたす方程式系の解について無限遠特異集合の交わる点の近くでの漸近的挙動を調べた。（22頁）

A system associated with the confluent hyper geometric function　Φ３ and a certain linear ordinary differential equation with two irregular singular points

SHIMOMURA SHUN

Internat. J. Math. 8   689–702 1997.08

Research paper (scientific journal), Single Work, Accepted

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合流型超幾何関数Φ３のみたす方程式系のみたす方程式系および2つの不確定特異点をもつ線形方程式の解についてその大域的な性質を調べた。（14頁）

An initial value problem associated with a Painlevé equation on the positive real axis

SHIMOMURA SHUN

Nonlinear Anal. Proceedings of the Second World Congress of Nonlinear Analysts, Part 4 (Athens, 1996) 30   2161–2168 1997

Research paper (scientific journal), Single Work, Accepted

Connection formulae for solution of a system of partial differential equations associated with the confluent hyper geometric function　Φ２

SHIMOMURA SHUN

Proc.Japan Acad. Ser.A 72   82–84 1996.04

Research paper (scientific journal), Single Work, Accepted

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合流型超幾何関数f２のみたす方程式系のみたす方程式系の解に関する接続公式を求めた。（3頁）

On a generalized Bessel function of two variables,Ⅰ

SHIMOMURA SHUN

J.Math. Anal. Appl. 187   468–484 1994.10

Research paper (scientific journal), Single Work, Accepted

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二変数Bessel関数のみたす方程式系の解について無限遠特異集合の近くで漸近的挙動を明らかにした。（17頁）

Asympfotic expansions and Stokes multipliers of the confluent hyper geometric functionΦ２，Ⅰ

SHIMOMURA SHUN

Proc.Royal Soc. Edinbrgh 123   1165–1177 1993

Research paper (scientific journal), Single Work, Accepted

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合流型超幾何関数のみたす方程式系の解について無限遠特異集合の近くでのふるまいを調べた。（13頁）

Some remarks on the fifth Painleve equation on the positive real axis

SHIMOMURA SHUN

Proc.Japan Acad. Ser.A 68   172–174 1992.09

Research paper (scientific journal), Single Work, Accepted

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Painleve（Ⅴ）型方程式の正の実軸上での解のふるまいを原点の近くで調べた。（3頁）

On the fixed singular points of Painlevé equations [translation of Sûgaku 39 (1987), no. 4, 289–304; Sugaku Expositions]

SHIMOMURA SHUN; Takano, Kyoichi; Yoshida, Setsuji

Sugaku Expositions 5   93–114 1992

Research paper (other academic), Joint Work, Accepted

On an asymptotic property of a nonlinear ordinary differential equation

SHIMOMURA SHUN

Tokyo J. Math. 14   329–340 1991

Research paper (scientific journal), Single Work, Accepted

On solutions of the fifth Painlrve equation on the positive real axis

SHIMOMURA SHUN

Equation differentielles dans le champ complexe II(Strasbourg)(論文集)    39 - 57 1990.01

Research paper (conference, symposium, etc.), Single Work

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Painleve（Ⅲ）、（Ⅴ）の方程式について解を実軸上で調べた。（19頁）

Painleve方程式の動かない特異点について

高橋恭一,下村俊,吉田節治

数学 39   289–304 1987.10

Joint Work

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Painleve方程式の動かない特異点の近くでの解についての論説。（16頁）

On solutions of the fifth Painleve equation on the positive real axis　Ⅱ

SHIMOMURA SHUN

Funkcial.Ekvac. 30   203–224 1987.10

Research paper (scientific journal), Single Work, Accepted

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Painleve（Ⅴ）型方程式を正の実軸上での初期値問題の解が無限遠点近くでどのようにふるまうかを調べた。（22頁）

A family of solution of a nonlinear ordinary differential equation and its application to painleve equations(Ⅲ),(Ⅴ) and (Ⅵ)

SHIMOMURA SHUN

J.Math.Soc.Japan 39   649–662 1987.10

Research paper (scientific journal), Single Work, Accepted

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ある非線形方程式の確定型特異点における解の級数展開を求め、それをPainleve方程式に応用する事により比較的広い領域における級数解を求めた。（14頁）

On solutions of the fifth Painleve equation on the positive real axis　Ⅰ

SHIMOMURA SHUN

Funkcial.Ekvac. 28   341–370 1985.12

Research paper (scientific journal), Single Work, Accepted

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Painleve（Ⅴ）型方程式を正の実軸上で考え、無限遠点での解のふるまいおよび大域的な解について調べた。（30頁）

Analytil integration of some nonlinear ordinary differential equations and the fifth Painleve equation in the neigh bourhood of an irregular singular point

SHIMOMURA SHUN

Funkcial.Ekvac. 26   301–338 1983.12

Research paper (scientific journal), Single Work, Accepted

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動かない不確定得意点をもつ非線形常微分方程式及びPainleve方程式（Ⅴ）についてその近くでの解の展開式を求めた。（38頁）

Supplement to: "Series expansions of Painlevé transcendents in the neighbourhood of a fixed singular point''

SHIMOMURA SHUN

Funkcial. Ekvac. 25   363–371 1982

Research paper (scientific journal), Single Work, Accepted

Painlevé transcendents in the neighbourhood of fixed singular points

SHIMOMURA SHUN

Funkcial. Ekvac. 25   163–184 1982

Research paper (scientific journal), Single Work, Accepted

Series expansions of Painlevé transcendents in the neighbourhood of a fixed singular point.

SHIMOMURA SHUN

Funkcial. Ekvac. 25   185–197 1982

Research paper (scientific journal), Single Work, Accepted

Entire solutions of a polynomial difference equation

SHIMOMURA SHUN

J.Fac.Sci.Univ.Tokyo 28   253–266 1981.09

Research paper (scientific journal), Single Work, Accepted

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多項式型の差分方程式の解の複素解析的な性質について調べた。（14頁）

On a Pfaffian system containing Parameters

SHIMOMURA SHUN

Funkcial.Ekvac. 22   95–119 1979.04

Research paper (scientific journal), Single Work, Accepted

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パラメーターを含むPfaff方程式系の特異摂動問題の解について研究した。（25頁）