14 problems

Let $r_i$ be the fixed periodic integer sequence from the paper, and let $b(a)$ be the least endpoint $b$ for which the reduced denominator $v_{a,b}$ of…

For a positive integer $n$, let $H(1;n)=\sum_{k=1}^n1/k$, and for a prime $p$ let $J(1|p)$ denote the set of indices whose reduced numerator is divisible by $p$. Eswarathasan–Levin…

For the classical case $r_i=1$, let $b(a)$ denote the least integer $b$ for which the reduced denominator $v_{a,b}$ of $\displaystyle\sum_{i=a}^b\frac{1}{i}$ satisfies…

For integers $k,m\geq1$, define … Let $A_0,A_1,\dots$ and $B_0,B_1,\dots$ be the sequences defined in the paper. Uniform harmonic-sum asymptotics conjecture. For any $C\in(0,2)$ an…

NNNLO intercept coefficient conjecture. Each coefficient on the right-hand side is a linear combination with rational coefficients of binomial harmonic sums whose transcendentality…

Generalized triple-harmonic-sum conjecture.

The generalized alternating harmonic-sum conjecture.

Let $n>1$ be a positive integer, and let $p^{\alpha}\mathrel{\Vert}n$ be an odd prime power, meaning $p^{\alpha}\mid n$ and $p^{\alpha+1}\nmid n$, with $\alpha\geq1$. Let … where…

For positive integers $n>mgeq 1$ and primes $p>n$, define … Let $\mathcal{P}$ be the set of rational primes, let…

Strong uniqueness conjecture. Then there are constants $c_0,c_1,\ldots\in\mathbb{Q}$ such that, if $b_0,b_1,\ldots$ are defined by the generalized Wolstenholme coefficient construc…

Uniqueness conjecture. Then $b_j=b_{j,n}(k)$ for $j=0,1,\ldots,n$.

For a prime $p$, define … and let $J(p)$ be the set of positive integers $n$ such that $p$ divides the numerator of $H_n$ when written in reduced form. Erdős–Lehmer conjecture. The…

Let $p>3$ be a prime, and define … with $B_{p-5}$ the Bernoulli number of index $p-5$. Equivalent form of Sun's conjecture. … The paper states that this congruence is equivalent, v…

Let ${\sf N_{A,SH,H_1,H_2}}(l)$ denote the number of basis elements for the indicated classes of harmonic sums at cyclotomy $l$, and let the $(M)$-relations be the relations among…