Timeline for Function zeros in strip 0 < Re < 1 [closed]
Current License: CC BY-SA 2.5
14 events
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| Oct 17, 2011 at 22:00 | comment | added | Stopple | Mathematica does this easily, with FindRoot applied to an expression in HurwitzZeta, e.g. $s = 0.488705 - 0.510672 I$ | |
| Nov 14, 2010 at 22:48 | history | closed |
Robin Chapman user6976 Andrew Stacey Harald Hanche-Olsen Harry Gindi |
too localized | |
| Nov 14, 2010 at 21:37 | comment | added | Yemon Choi | eta: see my comment to Johan's answer. | |
| Nov 13, 2010 at 18:25 | comment | added | Yemon Choi | I should also add that phrasing such as "can you plz give me some zeros" is a bit off-putting to some of us. It makes it sound like you view us as your teachers or as your tech support | |
| Nov 13, 2010 at 17:05 | history | edited | Micah Milinovich |
edited tags
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| Nov 13, 2010 at 13:53 | history | edited | Gerry Myerson | CC BY-SA 2.5 |
corrected spelling
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| Nov 13, 2010 at 13:53 | comment | added | David E Speyer | I think the general point that Scott and I am making is that, if you just choose some random $a(n)$ and look at the zeroes of $\sum a(n)/n^s$, there is no reason to expect there to be any good control over the zeroes you get. The examples that work do so because they come from interesting cohomological or number theoretic constructions. Your function isn't even multiplicative, so it doesn't have an Euler product! (Note that $a(5)=-1$, $a(7)=-1$ and $a(35)=-1$.) I'm not one of the people voting to close, but I think that, without more motivation, you're not likely to get a better answer. | |
| Nov 13, 2010 at 13:52 | answer | added | Johan Andersson | timeline score: 24 | |
| Nov 13, 2010 at 13:12 | comment | added | S. Carnahan♦ | I don't think modern mathematics is ready for your question. It might help if you told us where you got your function, and what you would get out of a description of the zeroes in the critical strip. | |
| Nov 13, 2010 at 13:03 | comment | added | user6976 | There should be some motivation. Why do you want information about this combination of Dirichlet L-functions? | |
| Nov 13, 2010 at 12:53 | history | edited | Pietro Majer | CC BY-SA 2.5 |
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| Nov 13, 2010 at 12:44 | comment | added | David E Speyer | I don't think there will be any good description of the zeroes of this function. If you made $a(n)$ be $-1$ if $n$ is $-1$ modulo one of $3$ and $4$, but $1$ if $n$ is $-1$ mod both of them, then this would be some simple modification of the $L$-function for a Dirichlet character modulo $12$. But, as is, this is some linear combination of $L$ functions, so I don't see any way to understand its zeroes. | |
| Nov 13, 2010 at 12:15 | comment | added | Robin Chapman | Ouch, I thought at first that this reduced to RH but now I'm not so sure. It would also help if it were translated into English: my dictionary lacks "plz" for instance. | |
| Nov 13, 2010 at 12:02 | history | asked | eta | CC BY-SA 2.5 |