Timeline for Better trigonometrical inequalities for $\zeta(s)$?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2020 at 21:06 | comment | added | user142929 | I would like to add a reference if it is useful for you (I do not know if it is relevant/useful for this post, because I am not a professional mathematician). I know that there is a section that maybe you know (first paragraph of section 5) of the paper by Kevin Ford, Zero-free Regions for the Riemann Zeta Function, Number Theory for the Millenium II, A K Peters (2002). Maybe the author have some information in his homepage. Thus I don't know if my comment is relevant for your question/work, isn't required a response. | |
| Feb 5, 2020 at 22:39 | vote | accept | H A Helfgott | ||
| Feb 5, 2020 at 20:43 | answer | added | Terry Tao | timeline score: 17 | |
| Feb 5, 2020 at 19:46 | comment | added | H A Helfgott | @Lucia: what I have in mind is actually just to improve explicit bounds on $1/\zeta(\sigma+it)$ for $\sigma>1$ (so as to improve explicit bounds on $1/\zeta(1+it)$). Or would a better zero-free region necessarily follow from an inequality such as the one I request? | |
| Feb 5, 2020 at 19:30 | history | edited | H A Helfgott | CC BY-SA 4.0 |
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| Feb 5, 2020 at 19:29 | comment | added | H A Helfgott | I should have said $b_0=0$. | |
| Feb 5, 2020 at 19:29 | comment | added | Carlo Beenakker | apologies, but I do not understand what difference the condition you added makes; in the example I gave in the answer box I have $k=i_0=3$, $a_0,a_1,a_2=1,2,3$, $b_0,b_1,b_2=1,2,3$, and $a_{3}=6$, $b_3=0$, so $a_0=1<3a_{i_0}/4=9/2$. | |
| Feb 5, 2020 at 19:12 | history | edited | H A Helfgott | CC BY-SA 4.0 |
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| Feb 5, 2020 at 19:12 | comment | added | H A Helfgott | I should have added that $a_0<a_{i_0}$. What would be useful would be $a_0< 3 a_{i_0}/4$, actually. | |
| Feb 5, 2020 at 19:00 | answer | added | Carlo Beenakker | timeline score: 5 | |
| Feb 5, 2020 at 18:58 | comment | added | Lucia | $1+\cos \theta \ge 0$; $99+100 \cos \theta +\cos 2\theta \ge 0$; $98+100\cos \theta +\cos (2\theta) + \cos (4\theta) \ge 0$ (didn't check the last one, but surely it's correct). Depends on what you're after? For zero free regions this is not the relevant criterion (one coefficient being sum of the others) -- presumably you've already looked at Kadiri, Stechkin ... | |
| Feb 5, 2020 at 17:27 | history | asked | H A Helfgott | CC BY-SA 4.0 |