ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 11 Dec 2013 13:05:18 +0100Sym^2 L-fcn via Dokchitser in Sagehttps://ask.sagemath.org/question/8056/sym2-l-fcn-via-dokchitser-in-sage/Hello,
I'm trying to do some numerical computations in Sage with the Sym^2 L-function of a weight k classical cusp form. Let's say I just work with the Ramanujan delta function. What I want is to build a function which gives me a plot of $L(1/2+it, sym^2 \Delta)$ along for $t \in R$. The sympow implementation is just for elliptic curves, so (tell me if I'm wrong) it seems that Dokchitser's L-function calculator is the way to go.
The problem is that I don't understand what to put for the parameters GammaV. The documentation doesn't explain what the input means. It just gives the examples [0] for Riemann zeta, and [0,1] for either an elliptic curve, or the delta function. But I can't figure out the general form of the input from these three examples. E.g. Delta and an elliptic curve E have different Gamma factors, so how are they the same here?
Beyond that, what should the weight be? I don't really understand automorphic forms on GL_3 enough to know what the weight of sym^2 Delta should be. Other than that, I think I can just mimic the documentation for $L(s, \Delta)$. But is there a better way to get this in Sage? I could always implement the approximate functional equation from scratch, but that seems like more work.
Suggestions?Thu, 07 Apr 2011 15:25:24 +0200https://ask.sagemath.org/question/8056/sym2-l-fcn-via-dokchitser-in-sage/Answer by John Cremona for <p>Hello,</p>
<p>I'm trying to do some numerical computations in Sage with the Sym^2 L-function of a weight k classical cusp form. Let's say I just work with the Ramanujan delta function. What I want is to build a function which gives me a plot of $L(1/2+it, sym^2 \Delta)$ along for $t \in R$. The sympow implementation is just for elliptic curves, so (tell me if I'm wrong) it seems that Dokchitser's L-function calculator is the way to go. </p>
<p>The problem is that I don't understand what to put for the parameters GammaV. The documentation doesn't explain what the input means. It just gives the examples [0] for Riemann zeta, and [0,1] for either an elliptic curve, or the delta function. But I can't figure out the general form of the input from these three examples. E.g. Delta and an elliptic curve E have different Gamma factors, so how are they the same here?</p>
<p>Beyond that, what should the weight be? I don't really understand automorphic forms on GL_3 enough to know what the weight of sym^2 Delta should be. Other than that, I think I can just mimic the documentation for $L(s, \Delta)$. But is there a better way to get this in Sage? I could always implement the approximate functional equation from scratch, but that seems like more work.</p>
<p>Suggestions?</p>
https://ask.sagemath.org/question/8056/sym2-l-fcn-via-dokchitser-in-sage/?answer=15794#post-id-15794Try looking at the ComputeL web page at [http://www.maths.bris.ac.uk/~matyd/computel/index.html](http://www.maths.bris.ac.uk/~matyd/computel/index.html) and if that does not help, email its author Tim Dokchitser.
Wed, 11 Dec 2013 13:05:18 +0100https://ask.sagemath.org/question/8056/sym2-l-fcn-via-dokchitser-in-sage/?answer=15794#post-id-15794