5 problems

Let $theta otinboldsymbol{Q}$ and let $4mathsf{x}={xn}n$ with $xn=ntheta$. For a continuous function $f$, write … We say that these averages fluctuate when they are infinitely ofte…

Euler Sudler-product central limit conjecture. For every $t\in\mathbb R$,

Variance growth conjecture. The variance satisfies $\log M\ll B_M^2\ll\log M$. This accompanies a proved central limit theorem with the natural centering and scaling; the source la…

Let $\alpha$ be a real irrational number and let … where $\mathbb{R}/\mathbb{Z}$ is identified with $[0,1)$ and ordered naturally. A consecutive $1$-difference is a difference…

Quadratic-irrational discrepancy relation conjecture. Such a relation should hold for every pair $(\alpha,\beta)$ with $\alpha$ quadratic irrational and…