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Algebraic independence of the periods of abelian integrals

K. G. Vasil'ev

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 511.364

Received: 16.02.1995
Revised: 18.11.1995

DOI: 10.4213/mzm1881

 English version: Mathematical Notes, 1996, 60:5, 510–518

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