7 problems

Generating-function conjecture. The dimensions of these spaces satisfy

Let $S_1=S_1(a,b,c,d;n)$ and $S_2=S_2(a,b,c,d;n)$ be the two summands obtained from the WZ seeds in the harmonic extension of the displayed series, and let $V_N(S_i)$ be their degr…

Let $q\geq 1$ be an integer, and let $H_k=\sum_{j=1}^k\frac{1}{j}$ denote the $k$th harmonic number. For rational numbers $\alpha_{q,2},\alpha_{q,3},\ldots,\alpha_{q,q+2}$, conside…

Eswarathasan–Levine conjecture. There are infinitely many harmonic primes.

Eswarathasan–Levine conjecture. The set $J_p$ is finite for all primes $p$.

For each integer $j\geq 1$, let $h_j(n)$ denote the $j$th iterated harmonic number, as defined in the paper. In particular, $h_j(1)=1$. Integrality conjecture. For each integer…

For integers $n\geq k\geq1$, define … and let $\nu_p$ denote the $p$-adic valuation. The logarithmic lower-bound conjecture. For any prime number $p$ and any integer $k\geq1$, ther…