Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T15:43:37.336Z Has data issue: false hasContentIssue false
  • English
  • Français

On the periods of Abelian functions in two variables

Published online by Cambridge University Press:  26 February 2010

D. W. Masser
D. W. Masser
Affiliation:
Department of Mathematics, The University, Nottingham
Get access

Extract

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

MSC classification

Secondary: 32N99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 97 - 107
Copyright
Copyright © University College London 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Baker, A.. “On the periods of the Weierstrass p–function”, Symposia Math. INDAM Rome, 1968 (Academic Press, London, 1970), 155–174.Google Scholar
2.Hardy, G. H. and Wright, E. M.. Introduction to the theory of numbers (Oxford 1938).Google Scholar
3.Lang, S.. Introduction to transcendental numbers (Addison-Wesley, Reading, Mass., 1966).Google Scholar
4.Masser, D. W.. “Linear forms in algebraic points of Abelian functions I, II.” Both to appear in Math. Proc. Cambridge Philos. Soc.Google Scholar
5.Masser, D. W.. “Linear forms in algebraic points of Abelian functions III.” To appear in Proc. London Math. Soc.Google Scholar
6.Schneider, Th.. “Zur Theorie der Abelschen Funktionen und Integrale”, J. reine angew. Math., 183 (1941), 110–128.CrossRefGoogle Scholar
7.Siegel, C. L.. Topics in complex function theory, Vol. Ill (Wiley-Interscience, New York, 1973).Google Scholar
8.Swinnerton-Dyer, H. P. F.. Analytic theory of Abelian varieties (London Math. Soc. lecture notes 14, Cambridge, 1974).CrossRefGoogle Scholar
9.Waldschmidt, M.. Nombres transcendants (Springer-Verlag, Berlin, 1974).CrossRefGoogle Scholar
10.Weber, H.. Lehrbuch der Algebra, Vol. Ill (Chelsea Publishing Company, New York, 1958).Google Scholar