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Weyl closure of hypergeometric systems

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Abstract

We show that Ahypergeometric systems and Horn hypergeometric systems are Weyl closed for very generic parameters.

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References

  1. P. Appell, Sur les séries hypergéometriques de deux variables et sur des équations différentielles linéaires aux dérivées partielles,Comptes Rendus 90 (1880), 296–298.

    Google Scholar 

  2. A. Dickenstein, L. Felicia Matusevich, and E. Miller, BinomialD-modules, arXiv:math /0610353.

  3. A. Dickenstein, L. Felicia Matusevich, and E. Miller, Combinatorics of binomial primary decomposition,Math. Z., to appear.

  4. A. Dickenstein, L. Felicia Matusevich, and T. Sadykov, Bivariate hypergeometricD-modules,Adv. Math. 196 (2005), 78–123.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Eisenbud and B. Sturmfels, Binomial ideals,Duke Math. J. 84 (1996), 1–45.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Erdélyi, Hypergeometric functions of two variables,Acta Math. 83 (1950), 131–164.

    Article  MATH  MathSciNet  Google Scholar 

  7. K.G. Fischer and J. Shapiro, Mixed matrices and binomial ideals,J. Pure Appl. Algebra 113 (1996), 39–54.

    Article  MATH  MathSciNet  Google Scholar 

  8. I.M. Gel′fand, M.I. Graev, and A.V. Zelevinskiĭ, Holonomic systems of equations and series of hypergeometric type,Dokl. Akad. Nauk SSSR 295 (1987), 14–19.

    Google Scholar 

  9. I.M. Gel′fand, A.V. Zelevinskiĭ, and M.M. Kapranov, Hypergeometric functions and toric varieties,Funktsional. Anal. i Prilozhen 23 (1989), 12–26. CorrectionFunktsional. Anal. i Prilozhen 27 (1993), 91.

    Article  Google Scholar 

  10. D.R. Grayson and M.E. Stillman, Macaulay 2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.

  11. J. Horn, Über die konvergenz der hypergeometrischen Reihen zweier und dreier Veränderlichen,Math. Ann. 34 (1889), 544–600.

    Article  MathSciNet  Google Scholar 

  12. S. Hoşten and J. Shapiro, Primary decomposition of lattice basis ideals, Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998),J. Symbolic Comput. 29 (2000), 625–639.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Ohara and N. Takayama, Holonomic rank of Ahypergeometric differential difference equations,J. Pure Appl. Algebra, to appear.

  14. M. Saito, B. Sturmfels, and N. Takayama,Gröbner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics6, Springer-Verlag, Berlin, 2000.

    MATH  Google Scholar 

  15. H. Tsai,Algorithms for Algebraic Analysis, Doctoral dissertation, University of California at Berkeley, 2000.

  16. H. Tsai, Weyl closure of a linear differential operator, Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998)J. Symbolic Comput. 29 (2000), 747–775.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Tsai,Algorithms for associated primes, Weyl closure, and local cohomology of D-modules, Local cohomology and its applications (Guanajuato, 1999), 169–194. Lecture Notes in Pure and Appl. Math.226, 2002.

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Correspondence to Laura Felicia Matusevich.

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The author was partially supported by NSF Grant DMS 0703866.

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Felicia Matusevich, L. Weyl closure of hypergeometric systems. Collect. Math. 60, 147–158 (2009). https://doi.org/10.1007/BF03191207

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  • DOI: https://doi.org/10.1007/BF03191207

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