scholarly journals Generalized hypergeometric equations with certain finite irreducible monodromy groups

1989 ◽  
Vol 65 (7) ◽  
pp. 223-226
Author(s):  
Takao Sasai
Keyword(s):  
Monodromy Groups ◽  
Hypergeometric Equations

POLYNOMIALS ASSOCIATED WITH THE HYPERGEOMETRIC FUNCTIONS WITH FINITE MONODROMY GROUPS

2004 ◽  
Vol 15 (07) ◽  
pp. 629-649 ◽  
Author(s):  
HIROYUKI OCHIAI ◽  
MASAAKI YOSHIDA
Keyword(s):  
Hypergeometric Functions ◽  
Integral Parameter ◽  
Monodromy Groups ◽  
Hypergeometric Equations

The hypergeometric equations with polyhedral monodromy groups derive 3-integral-parameter families of polynomials.

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

Monodromy groups of critical point of functions

1982 ◽  
Vol 67 (1) ◽  
pp. 123-131 ◽  
Author(s):  
S. V. Chmutov
Keyword(s):  
Critical Point ◽  
Monodromy Groups

scholarly journals k-Hypergeometric Series Solutions to One Type of Non-Homogeneous k-Hypergeometric Equations

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 262 ◽  
Author(s):  
Shengfeng Li ◽  
Yi Dong
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Hypergeometric Series ◽  
Second Order ◽  
Series Solutions ◽  
Frobenius Method ◽  
General Solutions ◽  
Hypergeometric Differential Equation ◽  
Polynomial Term ◽  
Hypergeometric Equations

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

scholarly journals Monodromy groups of hypergeometric functions satisfying algebraic equations

2003 ◽  
Vol 55 (2) ◽  
pp. 189-205 ◽  
Author(s):  
Mitsuo Kato ◽  
Masatoshi Noumi
Keyword(s):  
Hypergeometric Functions ◽  
Algebraic Equations ◽  
Monodromy Groups
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