论文标题
在$ζ（1/2+it）$的时刻
On the moments of the moments of $ζ(1/2+it)$
论文作者
论文摘要
在$ [0，t] $上随机进行$ t $，我们考虑到$ k $ th的时间，相对于$ t $，是随机变量的$ t $，对应于$2β$ th的$ζ（1/2+ix）$上的$ζ（1/2+ix）$（t，t，t+1] $，其中$ζ$ riemann zeta nem riemann zeta nise nemery nemery nemery nemery nemery nemery nemery nemery nemery nem n herem nem rem' Zeta功能，并在整数$ k，β$的情况下，在$ t \ infty $的情况下提出了一个猜想。 snaith \ cite {cfkrs2}。 $ L $ - 功能。
Taking $t$ at random, uniformly from $[0,T]$, we consider the $k$th moment, with respect to $t$, of the random variable corresponding to the $2β$th moment of $ζ(1/2+ix)$ over the interval $x\in(t, t+1]$, where $ζ(s)$ is the Riemann zeta function. We call these the `moments of moments' of the Riemann zeta function, and present a conjecture for their asymptotics, when $T\to\infty$, for integer $k,β$. This is motivated by comparisons with results for the moments of moments of the characteristic polynomials of random unitary matrices and is shown to follow from a conjecture for the shifted moments of $ζ(s)$ due to Conrey, Farmer, Keating, Rubinstein, and Snaith \cite{cfkrs2}. Specifically, we prove that a function which, the shifted-moment conjecture of \cite{cfkrs2} implies, is a close approximation to the moments of moments of the zeta function does satisfy the asymptotic formula that we conjecture. We motivate as well similar conjectures for the moments of moments for other families of primitive $L$-functions.
