Geodesic
Zolotarev polynomials and reduction of Shabat polynomials into a positive characteristic
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 47-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMUMM_2016_6_a7,
     author = {D. A. Oganesyan},
     title = {Zolotarev polynomials and reduction of {Shabat} polynomials into a positive characteristic},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {47--51},
     year = {2016},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a7/}
}
TY  - JOUR
AU  - D. A. Oganesyan
TI  - Zolotarev polynomials and reduction of Shabat polynomials into a positive characteristic
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 47
EP  - 51
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a7/
LA  - ru
ID  - VMUMM_2016_6_a7
ER  - 
%0 Journal Article
%A D. A. Oganesyan
%T Zolotarev polynomials and reduction of Shabat polynomials into a positive characteristic
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 47-51
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a7/
%G ru
%F VMUMM_2016_6_a7
D. A. Oganesyan. Zolotarev polynomials and reduction of Shabat polynomials into a positive characteristic. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 47-51. http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a7/

[1] Zvonkin A.K., Lando S.K., Grafy na poverkhnostyakh i ikh prilozheniya, MTsNMO, M., 2011

[2] Oganesyan D., “Abel pairs and modular curves”, Zapiski nauchnykh seminarov POMI, 446, 2016, 165–181 | MR

[3] Vashevnik A.M., Pary Belogo nad konechnymi polyami i ikh reduktsiya, Kand. dis., M., 2006

[4] Kochetkov Yu.Yu., “Mnogochleny Chebysheva, mnogochleny Zolotareva i ploskie derevya”, Fund. i prikl. matem., 18:6 (2013), 161–170

[5] Hirzebruch F., Berger T., Jung R., Manifolds and Modular Forms, Vieweg-Verlag, Wiesbaden, 1992 | MR | Zbl

[6] Shabat G.B., “Mnimokvadratichnye resheniya antivandermondovykh sistem s 4 neizvestnymi i orbity Galua derevev diametra 4”, Fund. i prikl. matem., 9:3 (2003), 229–236 | MR | Zbl

[7] Kochetkov Yu., “Trees of diameter 4”, Proc. 12th Int. Conf., FPSAC'OO (Formal Power Series and Algebraic Combinatorics), eds. D. Krob, A. A. Mikhalev, A. V. Mikhalev, Springer, 2000, 447–475 | DOI | MR

[8] Dremov V.A., Vashevnik A.M., “O parakh Belogo nad proizvolnymi polyami”, Fund. i prikl. matem., 12:3 (2006), 3–8 | MR

[9] Vashevnik A.M., “Prostye plokhoi reduktsii detskikh risunkov roda 0”, Fund. i prikl. matem., 11:2 (2005), 25–43 | MR

[10] Couveignes J.-M., “Calcul et rationalé de fonctions de Belyi en genre 0”, Ann. Inst. Fourier (Grenoble), 44:1 (1994), 1–38 | DOI | MR | Zbl