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2 answers
230 views

What is the approximation of $\log(|\zeta'(\frac{1}{2}+it)|)$ in Dirichlet polynomial if it is exists?

I have done some search many times on web to find any approximation of $\log|(\zeta'(s))|$ in Dirichlet polynomial but I didn't got it, Probably that $\log(|\zeta'(s)|$ dosn't have a Dirichlet ...
zeraoulia rafik's user avatar
0 votes
0 answers
64 views

if $\max_{z \in K} |\zeta(z+it)-f(z)|<\epsilon.$ then is this $\lim_{t\to \infty} \inf \frac {|\zeta'(z+it)|}{|f'(z)|} $ a finit limit?

Universality theorem of Riemann zeta function states that :Let $K$ be a compact subset with connected complement lying in the strip $\{1/2 < \operatorname{Re}(z)<1\}$, and let $f : K \rightarrow ...
zeraoulia rafik's user avatar
1 vote
0 answers
108 views

Bounding quantiles of the noncentral chi distribution

I need to bound the empirical quantiles for a noncentral chi distribution (not chi-squared) $\chi_\nu(\lambda)$, where $\nu$ is the number of degrees of freedom and $\lambda$ the non-centrality ...
etal's user avatar
  • 162
4 votes
1 answer
232 views

Expectation over Pareto Sums

Given $K$ iid random variables $x_i$ with uniform distribution on $(0,1]$ and a constant $\alpha > 0$, the random variable $x_i^{-\alpha/2}$ is Pareto-distributed with scale parameter $1$ and ...
August.xxz's user avatar
3 votes
1 answer
679 views

using polynomials as lower / upper bound?

I'm interested in the question of given a differentiable and bounded function $f(\vec{x})$ (over a single variable or multiple variables, over a bounded domain $D$), finding a pair of polynomials $p_1(...
Evan Pu's user avatar
  • 195