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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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

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

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

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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

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