68 problems

Let $X$ be a pure or mixed motive defined over $\overline{\mathbb{Q}}$. Write $\mathrm{periods}(X)$ for its periods and $\mathcal{G}_{\mathrm{mot}}(X)$ for its motivic Galois group…

Let $\xi$ be a real number defined by a series of the form … for arbitrary $p/q\in\mathbb{Q}$ and positive integer parameters $z_2,z_3,\ldots$. Transcendence conjecture. Every such…

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

Transcendentality–multiplier group conjecture. A quasiperiodic flow $\psi$ is transcendental if and only if

Let $\mathbf{A}=\mathbb{F}_q[t]$, $A=\mathbb{F}_q[\theta]$, and $K=\operatorname{Frac}(A)=\mathbb{F}_q(\theta)$. Let $E$ be a finite extension of $K$ and let…

Bounded-support conjecture. The support $\operatorname{Supp}(f)$ must be a finite set.

Let $f$ be a non-exceptional polynomial of degree $d\ge 2$. Let $Z\subset \mathbb{D}_R^n\times U_\infty(f)^n$ be an analytic subset of dimension $0\le m\le n$ defined by the parame…

Let $\Gamma=\operatorname{PSL}_2(\mathbb{Z})$, let $\Gamma^\prime\subset\Gamma$ be a finite-index subgroup corresponding to a finite cover $\mathbf{M}^\prime\to\mathbf{M}$, and let…

Let $p_n$ denote the $n$th prime, and define … Let $\mathcal{C}_{\mathcal{A}}$ denote the subring of algebraic elements of $\mathcal{A}$. Transcendence conjecture. … The paper prov…

Let $\mathbf M$ be the set of values under consideration in the paper. For a complex number $\xi$ and a positive integer $d$, define $w_d(\xi)$ as the supremum of the real numbers…

Totient threshold conjecture. If $\varphi(M-1)/2\geq 2$, then $C_M$ does not admit a representation

Integral algebraicity conjecture. For every integer $q\geq 2$,

Algebraicity conjecture.

Fix an embedding $\iota_p:\overline{\mathbb{Q}}\hookrightarrow\overline{\mathbb{Q}}_p$, let $A$ be an abelian variety over $\overline{\mathbb{Q}}$ of dimension $d$, and let…

Let $n\in\mathbb{Z}_{\geq2}$ be fixed. For each $m\in\{2,3,\ldots,n\}$ and each $\theta\in\left(\mathcal{G}_{m}^{\left(\operatorname{U}\right)}\cup\{\gamma\}\right)$, let…

Let $\zeta(s_1,\ldots,s_r)$ be a multiple zeta value with $s_1>1$ and $s_2,\ldots,s_r\ge1$, and let its weight be $s_1+\cdots+s_r$. For $k\ge1$, define … and…

Chowla–Milnor conjecture. The set $\mathfrak{L}$ is linearly independent over $\mathbb{Q}$. The conjecture is important because its consequences include conditional irrationality r…

Let $fin \mathbb{Q}[[z]]$ be a globally bounded and D-finite power series, and let $L^{\mathrm{min}}_f$ denote its minimal annihilating differential operator. Christol–André conjec…

Let $\alpha^{(p)}$ be a p-adic quadratic irrational, and consider its Ruban continued fraction. Capuano–Veneziano–Zannier conjecture. The Ruban continued fraction of a quadratic ir…

Let $\mathbb{R}_{\mathrm{an},\exp}$ denote the real field expanded by restricted analytic functions and the exponential function. Let $f:\mathbb{R}\to\mathbb{R}$ be definable in…

Chatterjee–Garg conjecture. The numbers

Upsilon transcendence conjecture. Upsilon constants $\Upsilon_n$ are transcendental.

Stirling-Ramanujan transcendence conjecture. The Stirling-Ramanujan constants are transcendental.

Motivated Grothendieck period conjecture. The motive $M$ satisfies MGPC if $\Omega^{\mathrm{And}}_M$ is connected and

Conjecture sur les périodes des courbes elliptiques sans multiplication complexe. Les quatre périodes de $E$ sont algébriquement indépendantes.