6 problems

Let $f$ be a weight $k$ Maaß form for a general Fuchsian group $\Gamma$, let $\operatorname{Conj}(\Gamma)$ denote the conjugacy classes of $\Gamma$, and let…

Let $f$ be a weight $k$ Maaß form for a general Fuchsian group $\Gamma$, let $C_\Gamma(\log N)$ denote the relevant set of primitive hyperbolic conjugacy classes with trace bounded…

Let $X_1,X_2,\ldots,X_n$ be a random sample of size $n\geq 3$ from any distribution $F$ on $\mathbb{R}$. Write $\overline{X}_n$ for the sample mean and $G_n$ for Gini's mean differ…

Let $P$ be a probability satisfying the tilted-law property (TLP), and let $P_t$ denote its associated exponential family. Define … A median of $P_t$ is a real number $a$ such that…

Let $X_1,X_2,\dots,X_n$ be non-degenerate, independently and identically distributed classical random variables with finite non-zero variance $\sigma^2$, and let $\overline{X}$ den…

Let $\mu={\cal N}(0;1)$ be the standard normal distribution, let $(a^{(N)})_{N\geq 1}$ be a quadratic optimal greedy sequence for $\mu$, and let $e_{2,N}(\mu)$ denote the minimal q…