The Ramanujan Journal

, Volume 1, Issue 4, pp 339-350

First online:

Theta Functions and Transcendence

  • Daniel BertrandAffiliated withUniversité de Paris VI, Institut de Mathématiques

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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