Timeline for Function zeros in strip 0 < Re < 1
Current License: CC BY-SA 2.5
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| Nov 14, 2010 at 21:37 | comment | added | Yemon Choi | eta: in some cultures it is considered impolite to get other people to do your work for you, especially if you do not consider that they may have to spend effort on it. | |
| Nov 14, 2010 at 12:02 | history | edited | Johan Andersson | CC BY-SA 2.5 |
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| Nov 13, 2010 at 22:10 | comment | added | eta | so what are the first 10 zero's ? what are the first 10 zero's ( if any ) with real part = 1/2 ? thank you | |
| Nov 13, 2010 at 18:04 | history | edited | Johan Andersson | CC BY-SA 2.5 |
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| Nov 13, 2010 at 16:51 | comment | added | Johan Andersson | John, Thanks for your comment. I think you are right. I have listen to seminars of Dennis Hejhal on the subject, but not really worked on the problem myself. The use of Voronin universality to prove that there are $\gg T$ zeros for strips to the right on the critical line still holds though, so that RH is not true. I will change my answer to reflect this | |
| Nov 13, 2010 at 16:47 | comment | added | Micah Milinovich | (continued) I am currently without access to MathSciNet, but I believe Gonek has conjectured that $\zeta(s,a)$ has at $\ll T$ on the line Re $s=1/2$ is $a\neq 1/2$ is a rational number with $0<a<1$. | |
| Nov 13, 2010 at 16:44 | comment | added | Micah Milinovich | @Johan: The function $f(s)$ in the question can be written as a linear combination of Dirichlet L-functions, but it cannot be written as a linear combination of Dirichlet L-functions which all have the same functional equation (i.e. all of the same modulus and are all either even or odd). I believe that if you look at the results of Hejahl and of Bombieri & Hejhal, you will see that they are always assuming that the linear combination of L-functions satisfy to same functional equation. In particular, I do not believe that their results can be used to study the zeros of Hurwitz zeta-functions. | |
| Nov 13, 2010 at 16:38 | history | edited | Johan Andersson | CC BY-SA 2.5 |
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| Nov 13, 2010 at 15:43 | comment | added | David E Speyer | Well, so much for Scott and my pessimism. Nice answer! | |
| Nov 13, 2010 at 14:40 | history | edited | Johan Andersson | CC BY-SA 2.5 |
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| Nov 13, 2010 at 13:57 | history | edited | Johan Andersson | CC BY-SA 2.5 |
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| Nov 13, 2010 at 13:52 | history | answered | Johan Andersson | CC BY-SA 2.5 |