Riccati Differential Equation for Hypergeometric Differential Equation

Nakagawa, Takahiro

Nakagawa, Takahiro

Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012), p. 179-192 / Harvested from Numdam

Access to full text
Full (PDF)
Full (DJVU)

Publié le : 2012-01-01

MR 2978004 | Zbl 1278.12005

@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},
     volume = {128},
     year = {2012},
     pages = {179-192},
     mrnumber = {2978004},
     zbl = {1278.12005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2012__127__179_0}
}

Nakagawa, Takahiro. Riccati Differential Equation for Hypergeometric Differential Equation. Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012) pp. 179-192. http://gdmltest.u-ga.fr/item/RSMUP_2012__127__179_0/

Bibliographie

[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 2406119 | Zbl 1161.12002

[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 2737705 | Zbl 1221.14027

[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 2516304 | Zbl 1176.12006

[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 772749 | Zbl 0589.12020

[Dwork1] B. M. Dwork, On p-adic differential equations II, Annals of Math., 98, (2) (1973), pp. 366-376. | MR 572253 | Zbl 0304.14015

[Dwork2] B. M. Dwork, Lectures on $p$ -adic differential equations, Grundlehren Math. Wiss. 253, Springer- Verlag, New York-Berlin, 1982. | MR 678093 | Zbl 0502.12021

[DGS] B. Dwork - G. Gerotto - F. Sullivan, An Introduction to $G$ -Functions, Annals of Math. Studies 133, Princeton University Press, Princeton, 1994. | MR 1274045 | Zbl 0830.12004

[D-R] B. M. Dwork - P. Robba, On Ordinary Linear $p$ -Adic Differential Equations, T.A.M.S., 231 (1977), pp. 1-46. | MR 447247 | Zbl 0375.34010

[Kedlaya] K. Kedlaya, $p$ -adic differential equations, Cambridge University Press, Cambridge (2010). | MR 2663480 | Zbl 1213.12009

[Put] M. Van Der Put, Reduction modulo $p$ of differential equations. Indag. Math. N. S., 7, (3) (1996), pp. 367-387. | MR 1621401 | Zbl 0865.12007

[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 1908143 | Zbl 1004.12005

[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 1960772 | Zbl 1036.12008

[R-C] P. Robba - G. Christol, Équation différentielles $p$ -adiques. Application aux sommes exponentielles. Actualités Math., Hermann, Paris, 1994. | MR 1411447 | Zbl 0868.12006

[Robba] P. Robba, On the index of $p$ -adic differential operators I, Ann. of Math. (2), 101 (1975), pp. 280-316. | MR 364243 | Zbl 0316.12102

[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 2637315