An abelian analogue of Schanuel’s conjecture and applications

Authors

Patrice Philippon, CNRS Centre National de la Recherche Scientifique
Biswajyoti Saha, University of Hyderabad
Ekata Saha, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Ramanujan Journal

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.

First Page

381

Last Page

392

DOI

10.1007/s11139-019-00173-w

Publication Date

6-1-2020

Comments

Open Access, Green

Recommended Citation

Philippon, Patrice; Saha, Biswajyoti; and Saha, Ekata, "An abelian analogue of Schanuel’s conjecture and applications" (2020). Journal Articles. 287.
https://digitalcommons.isical.ac.in/journal-articles/287