Measures of simultaneous approximation for quasi-periods of abelian varieties

JOURNAL OF NUMBER THEORY

卷:94

Article

Grinspan, P

关键词: transcendence;    simultaneous approximation;    algebraic independence;    Chudnovsky;    periods;    second kind;    abelian varieties;    Weierstrass functions;    Eisenstein's theorem;    G-functions;   

DOI  :  10.1006/jnth.2001.2733

来源: Elsevier

【 摘 要 】

We examine various extensions of a series of theorems proved by Chudnovsky in the 1980s on the algebraic independence (transcendence degree 2) of certain quantities involving integrals of the first and second kind on elliptic curves; these extensions include generalizations to abelian varieties of arbitrary dimensions, quantitative refinements in terms of measures of simultaneous approximation, as well as some attempt at unifying the aforementioned theorems. In the process we develop tools that might prove useful in other contexts, revolving around explicit algebraic theta functions on the one hand, and Eisenstein's theorem and G-functions on the other hand. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free