6 problems

Let $V \subseteq \mathbb{C}^n \times (\mathbb{C}^{\times})^n$ be an algebraic subvariety. An exponential point of $V$ is a point of the form…

A complex number is exponentially algebraic if it is a root of a non-degenerate exponential-logarithmic system of equations. Non-exponential-algebraicity conjecture. … This conject…

Let $E\!L^{(e)}$ denote the purely exponential tower with base $e$. Lang's conjecture. … Serge Lang made this conjecture in 1966, and the source states that it was proved only cond…

Let $E\!L^{alg}$ be the field of algebraically based numbers, obtained from $\mathbb{Q}$ by repeatedly adjoining algebraic numbers, exponentials, and logarithms of previously gener…

Let ${\mathbb C}_{\exp}$ denote the field of complex numbers equipped with the exponential map. A system of exponential-sum equations is well-defined when it satisfies the relevant…

Schanuel Subset Conjecture. If the set $\{\alpha_1,\dotsc,\alpha_n,e^{\alpha_1},\dotsc,e^{\alpha_n}\}$ is $\overline{\mathbb{Q}}$-dependent on a subset $\{\beta_1,\dotsc,\beta_n\}$…