Theta Functions and Transcendence

  title={Theta Functions and Transcendence},
  author={D. Bertrand},
  journal={The Ramanujan Journal},
  • D. Bertrand
  • Published 1 December 1997
  • Mathematics
  • The Ramanujan Journal
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. 
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