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Sym^2 L-fcn via Dokchitser in Sage

asked 2011-04-07 15:25:24 +0200

Ian Petrow gravatar image


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.


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answered 2013-12-11 13:05:18 +0200

John Cremona gravatar image

Try looking at the ComputeL web page at and if that does not help, email its author Tim Dokchitser.

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Asked: 2011-04-07 15:25:24 +0200

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Last updated: Dec 11 '13