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Communications in Mathematical Physics

, Volume 363, Issue 3, pp 1081–1101 | Cite as

Determinant Structure for \({\tau}\)-Function of Holonomic Deformation of Linear Differential Equations

  • Masao Ishikawa
  • Toshiyuki Mano
  • Teruhisa Tsuda
Article
  • 43 Downloads

Abstract

In our previous works, a relationship between Hermite’s two approximation problems and Schlesinger transformations of linear differential equations has been clarified. In this paper, we study \({\tau}\)-functions associated with holonomic deformations of linear differential equations by using Hermite’s two approximation problems. As a result, we present a determinant formula for the ratio of \({\tau}\)-functions (\({\tau}\)-quotient).

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Acknowledgements

This work was supported by a grant-in-aid from the Japan Society for the Promotion of Science (Grant Numbers 16K05068, 17K05270, 17K05335, 25800082 and 25870234).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Masao Ishikawa
    • 1
  • Toshiyuki Mano
    • 2
  • Teruhisa Tsuda
    • 3
  1. 1.Department of MathematicsOkayama UniversityOkayamaJapan
  2. 2.Department of Mathematical SciencesUniversity of the RyukyusOkinawaJapan
  3. 3.Department of EconomicsHitotsubashi UniversityTokyoJapan

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