紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2014, 51(4), p. 867-903

A CLASSIFICATION OF COVERINGS YIELDING HEUN-TO-HYPERGEOMETRIC REDUCTIONS

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2014-10

Pull-back transformations between Heun and Gauss hypergeometric equations give useful expressions of Heun functions in terms of better understood hypergeometric functions. This article classifies, up to Möbius automorphisms, the coverings P1→ P1 that yield pull-back transformations from hypergeometric to Heun equations with at least one free parameter (excluding the cases with Liouvillian solutions). In all, 61 parametric hypergeometric-to-Heun transformations are found, of maximal degree 12. Among them, 28 are compositions of smaller degree transformations between hypergeometric and Heun functions. The 61 transformations are realized by 48 different Belyi coverings (though 2 coverings should be counted twice as their moduli field is quadratic). 38 of these coverings appear in Herfurtner’s list of elliptic surfaces over P1 with four singular fibers, as their j -invariants. In passing, we show in an elegant way that there are no coverings with some branching patterns.

10.18910/50975

50975

A CLASSIFICATION OF COVERINGS YIELDING HEUN-TO-HYPERGEOMETRIC REDUCTIONS

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-10

Osaka Journal of Mathematics

51

4

867

903

https://hdl.handle.net/11094/50975

10.18910/50975

https://doi.org/10.18910/50975