6 problems

Let $k,l\geqslant 2$ be natural numbers, let $h\in\mathbb{Z}\setminus\{0\}$, and let $d_k(n)$ and $d_l(n)$ denote the $k$-fold and $l$-fold divisor functions. Divisor correlation c…

Elliott-type correlation conjecture. If $P_1$ and $P_2$ are irreducible binary quadratic forms that are not multiples of each other, then they are good for vanishing of correlation…

Let $\mathcal{M}$ be the set of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ with $|f(n)|\leq 1$. For $f,g\in\mathcal{M}$, define … A function is non-pretentious when it is…

Let $f$ be a fixed primitive cusp form, holomorphic or Maass, and let $\lambda_f(n)$ denote its Hecke eigenvalue at $n$. Write $\mathcal{L}=\log X$. Integer correlation conjecture.…

Let $f$ be a fixed primitive cusp form, holomorphic or Maass, and let $\lambda_f(p)$ denote its Hecke eigenvalue at a prime $p$. Write $\mathcal{L}=\log X$. Prime correlation conje…

For a continuous TASEP on a ring with $n$ particles, let … be the stationary two-point correlation for an adjacent pair, where $a$ is arbitrary. The upper-right correlation conject…