5 problems

Let $v_0\in\mathbb{Z}^d\setminus\{0\}$, and suppose $\mathcal{L}^{p,q}_{x,v_0}(n)$ converges to $l\in\mathbb{R}$ with non-trivial convergence rate $\rho<0$ and irrationality measur…

Convergence conjecture. There is an irrational $\alpha$ with

Let … be Catalan's constant, and let $\mu(\beta(2))$ denote its irrationality measure. Irrationality-measure conjecture. The irrationality measure of Catalan's constant is … This i…

For an irrational real number $x$, its irrationality measure $mu(x)$ is the supremum of the real numbers $mu$ such that $|x-a/q|<q^{-mu}$ has infinitely many solutions in integers…

Let $e$ denote Euler's number, let $\pi$ denote the circle constant, and let $\mu(x)$ denote the irrationality measure of a real number $x$. Irrationality-measure conjecture for…