The four exponentials problem and Schanuel’s conjecture. (English) Zbl 1543.11060
Morel, Jean-Michel (ed.) et al., Mathematics going forward. Collected mathematical brushstrokes. Cham: Springer. Lect. Notes Math. 2313, 579-592 (2023).
The paper surveys some well-known conjectures and results in transcendental number theory involving exponential and logarithmic functions and their \(p\)-adic counterparts. In particular, Schanuel’s conjecture, Leopoldt’s conjecture, the four exponential conjecture, the six exponential theorem, and the five exponential theorem (and strong variants of the last three) are reviewed.
I should add that I find the author’s writing style a little odd. For instance, when referring to some major open problems in transcendence theory, which are considered out of reach by experts, they write “it is still open” or “it is not yet proved”. At the end it is written that “This original point of view of D. Roy suggests a promising approach to proving Schanuel’s conjecture.”
For the entire collection see [Zbl 1515.01005].
I should add that I find the author’s writing style a little odd. For instance, when referring to some major open problems in transcendence theory, which are considered out of reach by experts, they write “it is still open” or “it is not yet proved”. At the end it is written that “This original point of view of D. Roy suggests a promising approach to proving Schanuel’s conjecture.”
For the entire collection see [Zbl 1515.01005].
Reviewer: Vahagn Aslanyan (Manchester)
MSC:
| 11J81 | Transcendence (general theory) |
References:
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