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3 questions
6
votes
1
answer
568
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Can one show that $|\zeta'(x) / \zeta^2(x)| \leq 1/(x-.5)$ for $x\in\mathbb{R}\cap [1,\infty)$?
I have found that $\left|\frac{\zeta'(x)}{\zeta^2(x)}\right|\leq \frac{1}{x-\frac{1}{2}}$ for all real $x$ such that $x>1$ seems to be true. I have plotted the inequality and got this inequality ...
- 178
1
vote
1
answer
288
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Bounding Coefficients of Dirichlet Series
Consider the exponentiated Riemann-Zeta function $\zeta(s)^p$. If it is represented as
$$\zeta(s)^p = \sum_{n=1}^\infty\frac{a_n}{n^s}$$
Is there any upper bound we can put on $|a_n|$ in terms of ...
- 1,129
0
votes
2
answers
364
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Can one show $\left|\frac{2(\zeta'(x))^2-\zeta''(x)\zeta(x)}{\zeta^3(x)}\right|\leq \frac{2}{(x-\frac{1}{2})^2}$ for $x\in\mathbb{R}\cap [1,\infty)$?
I have found that $\left|\frac{2(\zeta'(x))^2-\zeta''(x)\zeta(x)}{\zeta^3(x)}\right|\leq \frac{2}{(x-\frac{1}{2})^2}$ for all real $x$ such that $x>1$ seems to be true. I have plotted the ...
- 178