On classical irregular q-difference equations
نویسندگان
چکیده
منابع مشابه
On classical irregular q-difference equations
The primary aim of this paper is to (provide tools in order to) compute Galois groups of classical irregular q-difference equations. We are particularly interested in quantizations of omnipresent differential equations in the mathematical and physical literature, namely confluent generalized q-hypergeometric equations and q-Kloosterman equations.
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We present algorithm qHyper for finding all solutions y(x) of a linear homogeneous q-difference equation, such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and definite q-hypergeometric summation in closed form. ∗The research described in this publication was made possible in part by Grant J12100 from t...
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— The words “monodromy” and “isomonodromy” are used in the theory of difference and q-difference equations by Baranovsky-Ginzburg, Jimbo-Sakai, Borodin, Krichever,... although it is not clear that phenomena of branching during analytic continuation are involved there. In order to clarify what is at stake, we survey results obtained during the last few years, mostly by J.-P. Ramis, J. Sauloy and...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2012
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x12000292