The Ramanujan Journal

, Volume 1, Issue 4, pp 339–350 | Cite as

Theta Functions and Transcendence

  • Daniel Bertrand


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 


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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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