Theta functions and transcendence

被引：1
|
作者：
Bertrand D. [1 ]
机构：
[1] Université de Paris VI, Institut de Mathématiques, T. 46, 75 252 Paris Cédex 05, C. 247, 4, Place Jussieu
来源：
The Ramanujan Journal | 1997年 / 1卷 / 4期
关键词：
Algebraic independence; Modular forms;
D O I：
10.1023/A:1009749608672
中图分类号：
学科分类号：
摘要：
We transcribe in terms of theta functions the present state of knowledge on the transcendence degree of the fields generated by periods of elliptic integrals, or equivalently, by values of modular or hypergeometric functions. This approach leads to sharpenings of some of the quantitative aspects of the proofs. We conclude with a conjectural modular analogue of the Lindemann-Weierstrass theorem. © 1997 Kluwer Academic Publishers.
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页码：339 / 350
页数：11
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