Abstract:
The paper is focused on the study of Shabat polynomials over fields of different characteristics and their deformation into polynomials with three critical values. Using this deformation, we obtain prime numbers of bad reduction for Shabat polynomials corresponding to trees of diameter 4.
Key words:Shabat polynomials, Zolotarev polynomials, Belyi pairs, field of positive characteristic, reduction to positive characteristic.
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