Riccati Differential Equation for Hypergeometric Differential Equation

Nakagawa, Takahiro

Nakagawa, Takahiro

Rendiconti del Seminario Matematico della Università di Padova, Tome 127 (2012), pp. 179-192.

MR Zbl

@article{RSMUP_2012__127__179_0,
     author = {Nakagawa, Takahiro},
     title = {Riccati {Differential} {Equation} for {Hypergeometric} {Differential} {Equation}},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {179--192},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {127},
     year = {2012},
     mrnumber = {2978004},
     zbl = {1278.12005},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2012__127__179_0/}
}

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EP  - 192
VL  - 127
PB  - Seminario Matematico of the University of Padua
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%A Nakagawa, Takahiro
%T Riccati Differential Equation for Hypergeometric Differential Equation
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2012
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%I Seminario Matematico of the University of Padua
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%G en
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Nakagawa, Takahiro. Riccati Differential Equation for Hypergeometric Differential Equation. Rendiconti del Seminario Matematico della Università di Padova, Tome 127 (2012), pp. 179-192. http://www.numdam.org/item/RSMUP_2012__127__179_0/

Bibliographie
Cité par

[Andre] Y. André, Dwork’s conjecture on the logarithmic growth of solutions of $p$ -adic differential equations, Compos. Math., 144 (2008), pp. 484-494. | MR | Zbl

[Baldassarri] F. Baldassarri, Continuity of the radius of convergence of differential equations on p-adic analytic curves, Invent. Math., 182, (3) (2010), pp. 513-584. | MR | Zbl

[C-T] B. Chiarellotto - N. Tsuzuki, Logarithmic growth and Frobenius filtrations for solutions of p-adic differential equations, J. Inst. Math. Jussieu, 8 (2009), pp. 465-505. | MR | Zbl

[Christol] G. Christol, Modules différentiels et équations différentielles $p$ -adiques, Queen's Papers in Pure and Appl. Math. 66, Queen's University, Kingston, ON, 1983. | MR | Zbl

[Dwork1] B. M. Dwork, On p-adic differential equations II, Annals of Math., 98, (2) (1973), pp. 366-376. | MR | Zbl

[Dwork2] B. M. Dwork, Lectures on $p$ -adic differential equations, Grundlehren Math. Wiss. 253, Springer- Verlag, New York-Berlin, 1982. | MR | Zbl

[DGS] B. Dwork - G. Gerotto - F. Sullivan, An Introduction to $G$ -Functions, Annals of Math. Studies 133, Princeton University Press, Princeton, 1994. | MR | Zbl

[D-R] B. M. Dwork - P. Robba, On Ordinary Linear $p$ -Adic Differential Equations, T.A.M.S., 231 (1977), pp. 1-46. | MR | Zbl

[Kedlaya] K. Kedlaya, $p$ -adic differential equations, Cambridge University Press, Cambridge (2010). | MR | Zbl

[Put] M. Van Der Put, Reduction modulo $p$ of differential equations. Indag. Math. N. S., 7, (3) (1996), pp. 367-387. | MR | Zbl

[Put2] M. Van Der Put, Grothendieck’s conjecture for the Risch equation $y^{'} = a y + b$ . Indag. Math. (N.S.), 12 (2001), pp. 113-124. | MR | Zbl

[Put3] M. Van Der Put, Bounded $p$ -adic differential equations Circumspice, Nijmegen, 2001.

[PS] M. Van Der Put - M. Singer, Galois theory of linear differential equations. Grundlehren der Mathematischen Wissenschaften 328. Springer 2003. | MR | Zbl

[R-C] P. Robba - G. Christol, Équation différentielles $p$ -adiques. Application aux sommes exponentielles. Actualités Math., Hermann, Paris, 1994. | MR | Zbl

[Robba] P. Robba, On the index of $p$ -adic differential operators I, Ann. of Math. (2), 101 (1975), pp. 280-316. | MR | Zbl

[Young] P. Young, Radii of $p$ -adic convergence of generic solutions of homogeneous linear differential equations. Thesis (Ph.D.)-Oklahoma State University (1988), pp. 71. | MR