Timeline for Does it exist a p-adic L function which interpolates the values of the complex one at positive integers?
Current License: CC BY-SA 4.0
7 events
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| Jun 20, 2018 at 19:45 | history | edited | Ricky | CC BY-SA 4.0 |
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| Mar 1, 2016 at 13:06 | answer | added | Myshkin | timeline score: 2 | |
| Nov 22, 2010 at 18:55 | comment | added | Robin Chapman | If you do that, then basically you have the values at the negative integers. | |
| Nov 22, 2010 at 18:34 | comment | added | gvnros | I see your point, but if you multiply the $L$ function associated to the primitive character $L(k,\chi)$ by $i^a \pi^{1/2-k}\frac{\Gamma(\frac{k+a}{2})}{\Gamma(\frac{1-k+a}{2})}$, where $a$ is the parity of your character, then by the complex functional equation you know that it is algebraic. That is the number I would like to interpolate. Those are the numbers I would like to interpolate. Maybe the existence of a functional equation for the $p$-adic $L$ function could help | |
| Nov 22, 2010 at 18:23 | history | edited | gvnros | CC BY-SA 2.5 |
added 23 characters in body; edited title
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| Nov 22, 2010 at 16:40 | comment | added | Robin Chapman | Generally the values of L-functions at positive integers are transcendental numbers, or are numbers believed to be transcendental. There isn't a natural way to embed these iside an algebraic closure of $\mathbb{}_p$, so I cannot see how there's a sensible notion of interpolation. | |
| Nov 22, 2010 at 16:29 | history | asked | gvnros | CC BY-SA 2.5 |