13 problems

Lang–Rohrlich conjecture. The value $\Gamma(z)$ is algebraic if and only if

Let $\widehat{m}_{1/2}(x,\alpha)$ denote the logarithmic error term for the shifted interpolation parameter $\alpha$, let $\widehat{D}_{1/2}$ be its stated domain, and let…

The conjectured optimal logarithmic interpolation bound. For all $(x,\alpha)\in\widehat{D}$,

Let $n$ be a positive integer. For coordinate projections $\mathrm{Pr}_{\mathbf{i}}$ onto any selected $\ell$ pairs of coordinates, call an algebraic set…

Let $f_1,\ldots,f_n$ be holomorphic functions satisfying, for every distinct $i,j\in\{1,\ldots,n\}$, $f_i\notin\mathbb{Q}f_j+\mathbb{C}$. Write $\mathbf{f}=(f_1,\ldots,f_n)$ and…

Let $\tilde{\Gamma}(x)$ denote the principal branch of the inverse of the gamma function, so that $\tilde{\Gamma}(x)=y$ when $\Gamma(y)=x$. Let $\alpha=1.4616\ldots$ be the unique p…

Let $\pi_n$ denote the hyperelliptic constant associated with the index $n$. Let $n\in\mathbb{N}$ be composite and not a prime power, so that $n\neq p^m$ for $p\in\mathbb{P}$ and…

Gun–Ram Murty–Rath conjecture. The dimension of $\overline{V_{\Gamma}(q)}$ is

Gamma-quotient monotonicity conjecture. The quotient decreases as $c$ increases.

Let $a_1, a_2, \ldots, a_r$ be rational numbers that are not in $\{0, -1, -2, \ldots\}$. Let $D$ be a common denominator of the $a_i$'s. Rohrlich's conjecture. The product … is an…

The monotonicity conjecture. For every $\tau\geq0$, the function $g_\tau$ is strictly increasing on $(0,\infty)$. This conjecture is one of the monotonicity problems arising from r…

AVV conjecture. The function $H$ is increasing from $(1,\infty)$ into $(1/100,1/30)$. This conjecture is attributed to the authors' earlier work and is motivated by Ramanujan's rec…

Let $(v_n)_{n\geq 0}$ be the sequence of shifts appearing in the asymptotic expansion … The sequence begins with $v_1=\frac{23}{90}$, $v_2=\frac{1792627}{7289730}$, and…