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This article is cited in 8 scientific papers (total in 8 papers)
Fuchsian Equations with Three Non-Apparent Singularities
Alexandre Eremenkoa, Vitaly Tarasovbc a Purdue University, West Lafayette, IN 47907, USA
b St. Petersburg Branch of Steklov Mathematical Institute, St. Petersburg, 191023, Russia
c Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202, USA
Abstract:
We show that for every second order Fuchsian linear differential equation $E$ with $n$ singularities of which $n-3$ are apparent there exists a hypergeometric equation $H$ and a linear differential operator with polynomial coefficients which maps the space of solutions of $H$ into the space of solutions of $E$. This map is surjective for generic parameters. This justifies one statement of Klein (1905). We also count the number of such equations $E$ with prescribed singularities and exponents. We apply these results to the description of conformal metrics of curvature $1$ on the punctured sphere with conic singularities, all but three of them having integer angles.
Keywords:
Fuchsian equations; hypergeometric equation; difference equations; apparent singularities; bispectral duality; positive curvature; conic singularities.
Received: February 2, 2018; in final form June 10, 2018; Published online June 15, 2018
Citation:
Alexandre Eremenko, Vitaly Tarasov, “Fuchsian Equations with Three Non-Apparent Singularities”, SIGMA, 14 (2018), 058, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1357 https://www.mathnet.ru/eng/sigma/v14/p58
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Abstract page: | 205 | Full-text PDF : | 40 | References: | 16 |
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