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On the periods of Abelian functions in two variables

  • D. W. Masser (a1)


Let Λ be a lattice in Cn such that the field of Abelian functions on the quotient space Cn/Λ is of transcendence degree n. This implies that is an algebraic extension of a field o of pure transcendence degree n. Thus there exists a vector A = (A1 …, An) of algebraically independent functions of the variable z = (z1, …, zn) and a function B = B(z), algebraic over

such that



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1.Baker, A.. “On the periods of the Weierstrass p–function”, Symposia Math. INDAM Rome, 1968 (Academic Press, London, 1970), 155174.
2.Hardy, G. H. and Wright, E. M.. Introduction to the theory of numbers (Oxford 1938).
3.Lang, S.. Introduction to transcendental numbers (Addison-Wesley, Reading, Mass., 1966).
4.Masser, D. W.. “Linear forms in algebraic points of Abelian functions I, II.” Both to appear in Math. Proc. Cambridge Philos. Soc.
5.Masser, D. W.. “Linear forms in algebraic points of Abelian functions III.” To appear in Proc. London Math. Soc.
6.Schneider, Th.. “Zur Theorie der Abelschen Funktionen und Integrale”, J. reine angew. Math., 183 (1941), 110128.
7.Siegel, C. L.. Topics in complex function theory, Vol. Ill (Wiley-Interscience, New York, 1973).
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9.Waldschmidt, M.. Nombres transcendants (Springer-Verlag, Berlin, 1974).
10.Weber, H.. Lehrbuch der Algebra, Vol. Ill (Chelsea Publishing Company, New York, 1958).
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  • ISSN: 0025-5793
  • EISSN: 2041-7942
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