Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 056, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.056 (Mi sigma1852) 		 
This article is cited in 1 scientific paper (total in 1 paper)

$q$-Middle Convolution and $q$-Painlevé Equation

Shoko Sasakia, Shun Takagia, Kouichi Takemurab

a Department of Mathematics, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
b Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
Full-text PDF (443 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2022.056
Abstract: A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlevé VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlevé VI equation. We deduce an integral transformation on the $q$-Heun equation.
Keywords: $q$-Painlevé equation, $q$-Heun equation, middle convolution, integral transformation.
Funding agency Grant number
Japan Society for the Promotion of Science JP18K03378
The third author was supported by JSPS KAKENHI Grant Number JP18K03378.
Received: January 31, 2022; in final form July 8, 2022; Published online July 20, 2022
Bibliographic databases:
Document Type: Article
MSC: 33E10, 34M55, 39A13
Language: English
Citation: Shoko Sasaki, Shun Takagi, Kouichi Takemura, “$q$-Middle Convolution and $q$-Painlevé Equation”, SIGMA, 18 (2022), 056, 21 pp.
Citation in format AMSBIB
\Bibitem{SasTakTak22}
\by Shoko~Sasaki, Shun~Takagi, Kouichi~Takemura
\paper $q$-Middle Convolution and $q$-Painlev\'e Equation
\jour SIGMA
\yr 2022
\vol 18
\papernumber 056
\totalpages 21
\mathnet{http://mi.mathnet.ru/sigma1852}
\crossref{https://doi.org/10.3842/SIGMA.2022.056}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4454174}
Linking options:
  • https://www.mathnet.ru/eng/sigma1852
  • https://www.mathnet.ru/eng/sigma/v18/p56
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:41
    Full-text PDF :14
    References:11
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024