11 problems

Algebraic independence conjecture for odd zeta values. The numbers $\pi,\zeta(3),\zeta(5),\zeta(7),\zeta(9),\ldots$ are algebraically independent over $\mathbb{Q}$.

Algebraic-independence conjecture. The numbers $\ln p_1,\ldots,\ln p_m$ are algebraically independent. Equivalently, $\psi$ is an isomorphism.

Let $T_p(z)$ denote the valuation generating function associated with a prime $p$. Let $p_1,p_2,\dots,p_m$ be distinct primes, and let $\alpha_1,\alpha_2,\dots,\alpha_m$ be non-zer…

Let $r\geq 1$ be an integer. Let $b_1,\ldots,b_r$ be multiplicatively independent positive integers, and, for every $i$, $1\leq i\leq r$, let $\xi_i$ be a real number that is autom…

Let $\overline{\mathfrak{Z}}$ be the $\overline{\mathbb{Q}}$-algebra generated by multizeta values, and let $\overline{\mathfrak{Z}}_w$ be the $\overline{\mathbb{Q}}$-vector space…

Let $\alpha_1,\ldots,\alpha_n$ be non-zero algebraic numbers such that the numbers $\log \alpha_1,\ldots,\log \alpha_n$ are $\mathbb{Q}$-linearly independent. Weak Schanuel conject…

For $k\ge0$, let … be the $\calA_1$-Bernoulli numbers, and for $k\ge2$ let … be the $k$th $\calA_1$-Fermat quotient. Set $\gb_1=1$. Suppose $n_1,\dots,n_r\in\N$ and…

Let $\mathcal{L}$ be the $\mathbb Q$-vector space of logarithms of algebraic numbers: … For $n\geq 2$, let ${\sf LD}_n^{\mathbb Q}$ denote the relation of $n$ elements of…

Let $\Lambda\subset\mathbb{C}$ be a lattice, let $\lambda\in\Lambda\setminus\{0\}$, and let $\omega\in\mathbb{C}\setminus(\mathbb{Q}\lambda\cup\Lambda)$. Waldschmidt's conjecture.…

Let $\rho$ be a Drinfeld $\mathbb{F}_q[t]$-module defined over $\overline{k}$. Suppose $F_{\delta_1},\dots,F_{\delta_s}$ are quasi-periodic functions for $\mathbb{C}_\infty$-linear…

Magnus trace map surjectivity conjecture. The map $\mathsf{MagTr}_{\mathcal{I}}$ is surjective only for the cases