Timeline for construct a Hecke character in MAGMA with given infinity type

5 events

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Dec 8, 2015 at 20:05	comment	added	Jeremy Rouse		So, after playing with this for a while, it turns out you cannot do this in Magma. The form of the gamma factors in the Magma documentation is a typo - instead they are expected to be $\Gamma\left(\frac{s+\lambda_{1}}{2}\right) \cdots$. However, Magma expects the $\lambda_{i}$ to be rational, and this is a problem in your example! This is a factor of the Magma implementation - if you use Tim Dokchitser's original PARI script, you'll be fine. Another possibility is Michael Rubinstein's "lcalc".
Dec 8, 2015 at 18:31	comment	added	Ted Mao		Or, can you give me an example, say $\chi(\alpha)=Sgn(\alpha\bar{\alpha}) (\alpha\bar{\alpha}^{-1})^{i\pi/R}$ where $R$ is the regulator (so $\chi$ is 1 on the units), and $L(s)=\sum_{I\subset O_K} \chi(I) N(I)^{-s}$, where $K=\mathbb{Q}(\sqrt{3})$. In this case $\nu(s)=(d\pi^{-2})^{s/2} \Gamma(s/2+1/2+i\pi/2R)\Gamma(s/2+1/2-i\pi/2R)$
Dec 8, 2015 at 18:23	comment	added	Ted Mao		Thanks for the information. However, I am still confused about my case. The "General L-series" Magma page has an assumption on the gamma factor $\nu(s)=\Gamma(s+\lambda_1 /2)\ldots\Gamma(s+\lambda_d /2)$. Now we just have real places and there will be $\Gamma(s/2)$ type factors only. Does it still work?
Dec 8, 2015 at 16:29	vote	accept	Ted Mao
Dec 8, 2015 at 13:44	history	answered	Jeremy Rouse	CC BY-SA 3.0