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An abelian analogue of Schanuel’s conjecture and applications

  • Patrice Philippon
  • Biswajyoti SahaEmail author
  • Ekata Saha
Article
  • 37 Downloads

Abstract

In this article we study an abelian analogue of Schanuel’s conjecture. This conjecture falls in the realm of the generalised period conjecture of André. As shown by Bertolin, the generalised period conjecture includes Schanuel’s conjecture as a special case. Extending methods of Bertolin, it can be shown that the abelian analogue of Schanuel’s conjecture we consider also follows from André’s conjecture. Cheng et al. showed that the classical Schanuel’s conjecture implies the algebraic independence of the values of the iterated exponential function and the values of the iterated logarithmic function, answering a question of Waldschmidt. We then investigate a similar question in the setup of abelian varieties.

Keywords

Abelian analogue of Schanuel’s conjecture Linear disjointness Algebraic independence 

Mathematics Subject Classification

11J81 11J89 11J95 

Notes

Acknowledgements

The authors would like to thank D. Bertrand for helpful discussions and useful comments on an earlier version of this article. The second and the third authors would like to thank the Institut de Mathématiques de Jussieu for hospitality during academic visits in the frame of the IRSES Moduli and LIA. The authors would also like to thank the referee for helpful suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Patrice Philippon
    • 1
  • Biswajyoti Saha
    • 2
    Email author
  • Ekata Saha
    • 3
  1. 1.Équipe de Théorie des Nombres, Institut de Mathématiques de Jussieu-Paris Rive GaucheUMR CNRS 7586ParisFrance
  2. 2.School of Mathematics and StatisticsUniversity of HyderabadHyderabadIndia
  3. 3.Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia

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