Finite monodromy of Pochhammer equation

Yoshishige Haraoka

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 3, page 767-810
  • ISSN: 0373-0956

Abstract

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We consider the monodromy group G of the Pochhammer differential equation 𝒫 . Let 𝒫 p be the reduce equation modulo a prime p . Then we show that G is finite if and only if 𝒫 p has a full set of polynomial solutions for almost all primes p .

How to cite

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Haraoka, Yoshishige. "Finite monodromy of Pochhammer equation." Annales de l'institut Fourier 44.3 (1994): 767-810. <http://eudml.org/doc/75081>.

@article{Haraoka1994,
abstract = {We consider the monodromy group $G$ of the Pochhammer differential equation $\{\cal P\}$. Let $\{\cal P\}_p$ be the reduce equation modulo a prime $p$. Then we show that $G$ is finite if and only if $\{\cal P\}_p$ has a full set of polynomial solutions for almost all primes $p$.},
author = {Haraoka, Yoshishige},
journal = {Annales de l'institut Fourier},
keywords = {Grothendieck’s zero -curvature conjecture; Okubo system; equations free from accessory parameters; Pochhammer equation; apparent singular point; monodromy group},
language = {eng},
number = {3},
pages = {767-810},
publisher = {Association des Annales de l'Institut Fourier},
title = {Finite monodromy of Pochhammer equation},
url = {http://eudml.org/doc/75081},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Haraoka, Yoshishige
TI - Finite monodromy of Pochhammer equation
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 3
SP - 767
EP - 810
AB - We consider the monodromy group $G$ of the Pochhammer differential equation ${\cal P}$. Let ${\cal P}_p$ be the reduce equation modulo a prime $p$. Then we show that $G$ is finite if and only if ${\cal P}_p$ has a full set of polynomial solutions for almost all primes $p$.
LA - eng
KW - Grothendieck’s zero -curvature conjecture; Okubo system; equations free from accessory parameters; Pochhammer equation; apparent singular point; monodromy group
UR - http://eudml.org/doc/75081
ER -

References

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  2. [2] D.V. CHUDNOVSKY, G.V. CHUDNOVSKY, Applications of Padé approximations to the Grothendieck conjecture on linear differential equations. Lecture Notes in Math. 1135, 52-100, Springer, 1985. Zbl0565.14010MR87d:11053
  3. [3] Y. HARAOKA, Number theoretic study of Pochhammer equation. Publ. Math. de l'Université de Paris VI, Problèmes diophantiens, 93 (1989/1990). 
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  14. [14] T. SASAI, S. TSUCHIYA, On a fourth order Fuchsian differential equation of Okubo type, Funk. Ekvac., 34 (1991), 211-221. Zbl0744.34011MR93c:34015
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