3 problems

Let $b(n)$ be the indicator of the positive integers representable as sums of two squares, and let $q$ be a fixed positive integer. Connors–Keating conjecture. There is a precise p…

Let $b(n)$ be the indicator of sums of two squares. For an odd prime $p$, the Connors–Keating correlation conjecture specializes to the following explicit local factors. Connors–Ke…

H. Cohn's conjecture. Then $f$ is a multiplicative character on $\mathbb{F}_p$. This problem is still open in the finite-field setting; partial results are known, but the conjectur…