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Currently displaying 1 – 2 of 2

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Finite monodromy of Pochhammer equation

Yoshishige Haraoka — 1994

Annales de l'institut Fourier

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 $p$ .

Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka — 2012

Banach Center Publications

For a Fuchsian system $d Y / d x = (\sum_{j =}^{p} (A_{j}) / (x - t_{j})) Y$ , (F) $t ₁, t ₂, . . ., t_{p}$ being distinct points in ℂ and $A ₁, A ₂, . . ., A_{p} \in M (n \times n; ℂ)$ , the number α of accessory parameters is determined by the spectral types $s (A ₀), s (A ₁), . . ., s (A_{p})$ , where $A ₀ = - \sum_{j = 1}^{p} A_{j}$ . We call the set $z = (z ₁, z ₂, . . ., z_{α})$ of α parameters a regular coordinate if all entries of the $A_{j}$ are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues of the matrices...

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