The Ramanujan Journal

, Volume 1, Issue 4, pp 339–350

Theta Functions and Transcendence

  • Daniel Bertrand

DOI: 10.1023/A:1009749608672

Cite this article as:
Bertrand, D. The Ramanujan Journal (1997) 1: 339. doi:10.1023/A:1009749608672


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.

modular forms algebraic independence 

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Daniel Bertrand
    • 1
  1. 1.Université de Paris VI, Institut de MathématiquesParis Cédex 05

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