Irregular modified $A$-hypergeometric systems
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- by Francisco-Jesús Castro-Jiménez, María-Cruz Fernández-Fernández, Tatsuya Koike and Nobuki Takayama PDF
- Trans. Amer. Math. Soc. 367 (2015), 5415-5445 Request permission
Abstract:
A modified $A$-hypergeometric system is a system of differential equations for the function $f(t^w \cdot x)$, where $f(y)$ is a solution of an $A$-hypergeometric system in $n$ variables and $w$ is an $n$-dimensional integer vector, which is called the weight vector. We study the irregularity of modified systems by adapting to this case the notion of umbrella introduced by M. Schulze and U. Walther. Especially, we study slopes and Gevrey series solutions. We develop some applications of this study. Under some conditions we give Laplace integral representations of divergent series solutions of the modified system and we show that certain Gevrey series solutions of the original $A$-hypergeometric system along coordinate varieties are Gevrey asymptotic expansions of holomorphic solutions of the $A$-hypergeometric system.References
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Additional Information
- Francisco-Jesús Castro-Jiménez
- Affiliation: Department of Algebra, University of Sevilla, Seville, Spain
- Email: castro@us.es
- María-Cruz Fernández-Fernández
- Affiliation: Department of Algebra, University of Sevilla, Seville, Spain
- Email: mcferfer@us.es
- Tatsuya Koike
- Affiliation: Department of Mathematics, University of Kobe, Kobe, Japan
- Email: koike@math.kobe-u.ac.jp
- Nobuki Takayama
- Affiliation: Department of Mathematics, University of Kobe, Kobe, Japan
- Email: takayama@math.kobe-u.ac.jp
- Received by editor(s): September 9, 2012
- Received by editor(s) in revised form: May 28, 2013
- Published electronically: November 24, 2014
- Additional Notes: The first and second authors were partially supported by MTM2010-19336 and FEDER and Junta de Andalucía FQM5849, FQM333
The first author was also partially supported by S-13025-JSPS (Japan)
The second author was also partially supported by Max Planck Institute für Mathematik (Bonn)
The third author was partially supported by JSPS grants-in-aid No. 21740098 and No. S-24224001. - © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 5415-5445
- MSC (2010): Primary 32C38, 14F10; Secondary 33C70, 13N10, 14M25
- DOI: https://doi.org/10.1090/S0002-9947-2014-06225-9
- MathSciNet review: 3347178