منابع مشابه
Deformations of Fuchsian Equations
— We prove that the dimension of the deformations of a given generic Fuchsian system without changing the conjugacy class of its local monodromies (“number of accessory parameters”) is equal to half the dimension of the moduli space of deformations of the associated local system. We do this by constructing a weight 1 Hodge structure on the infinitesimal deformations of integrable connections. W...
متن کاملFinite-gap Solutions of the Fuchsian Equations
We find a new class of the Fuchsian equations, which have an algebraic geometric solutions with the parameter belonging to a hyperelliptic curve. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Numerous examples are given. Introduction Integrability of the Heun equation with half-odd characteristic exponents dy dz + P (z) dy dz +Q(z)y = 0, (0.1)...
متن کاملGalois theory of fuchsian q-difference equations
We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff’s classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger’s type.
متن کاملDifferential Equations Associated with Nonarithmetic Fuchsian Groups
We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an S-integral solution. These differential operators are naturally associated with Teichmüller curves in genus 2. They are counterexamples to conjectures by Chudnovsky–Chudnovsky and Dwork. We also det...
متن کاملFuchsian differential equations from modular arithmetic
Counting combinatorial objects and determining the associated generating functions can be computationally very difficult and expensive when using exact numbers. Doing similar calculations modulo a prime can be orders of magnitude faster. We use two simple polygon models to illustrate this: we study the generating functions of (singly) punctured staircase polygons and imperfect staircase polygon...
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ژورنال
عنوان ژورنال: Communications in Number Theory and Physics
سال: 2007
ISSN: 1931-4523,1931-4531
DOI: 10.4310/cntp.2007.v1.n2.a3