Geodesic
Algebraic independence of the periods of abelian integrals
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 681-691 Cet article a éte moissonné depuis la source Math-Net.Ru

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Abelian integrals of the first and the second kind are proved to have two algebraically independent periods. Some corollaries concerning the algebraic independence of the values of Euler's beta and gamma functions at rational points are derived. 
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K. G. Vasil'ev. Algebraic independence of the periods of abelian integrals. Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 681-691. http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a3/

[1] Mamford D., Lektsii o teta-funktsiyakh, Mir, M., 1988

[2] Chebotarev N. G., Teoriya algebraicheskikh funktsii, Gostekhizdat, M.–L., 1948

[3] Schneider T., “Zur Theorie der Abelschen Funktionen und Integrale”, J. Reine Angew. Math., 183:2 (1941), 110–128 | MR | Zbl

[4] Chudnovskii G. V., “Algebraicheskaya nezavisimost postoyannykh, svyazannykh s eksponentsialnoi i ellipticheskoi funktsiyami”, Dokl. AN USSR. Ser. A, 1976, no. 8, 697–700

[5] Waldschmidt M., “Les travaux de G. V. Chudnovskii sur les nombres transcendants”, Lecture Notes in Math., 567, Springer, Berlin, 1977, 274–292 | MR

[6] Laurent M., Sur la transcendance du rapport de deux integrales euleriennes, Progress in Math., 31, 1983 | MR | Zbl

[7] Feldman N. I., Sedmaya problema Gilberta, Izd-vo MGU, M., 1982 | Zbl

[8] Shidlovskii A. B., Transtsendentnye chisla, Nauka, M., 1987

[9] Masser D. W., “On the periods of abelian functions in two variables”, Mathematika, 22:2 (1975), 97–107 | MR | Zbl

[10] Shmidt V., Diofantovy priblizheniya, Mir, M., 1983

[11] Masser D. W., “The transcendence of certain quasi-periods associated with abelian functions in two variables”, Compositio Math., 35:3 (1977), 239–258 | MR | Zbl

[12] Masser D. W., “Diophantine approximation and lattices with complex multiplication”, Invent. Math., 45 (1978), 61–82 | DOI | MR | Zbl

[13] Brownawell W. D., “Gelfond's method for algebraic independence”, Trans. Amer. Math. Soc., 210 (1975), 1–26 | DOI | MR | Zbl

[14] Waldschmidt M., Nombres transcendants et groupes algebriques, Asterisque, 69–70, Soc. Math. France, 1979 | MR