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Sep 13 at 15:28 answer added Will Sawin timeline score: 3
Sep 13 at 15:06 history edited FeiHou CC BY-SA 4.0
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Sep 13 at 14:39 comment added FeiHou @DavidLoeffler Thanks for comment. Yes, it looks a bit strange; I am afraid that this type of $L$-series probably do not satisfy certain functional equation of the Riemann-type. Maybe one should consider $L(\Pi, s)=\sum_{n\ge 1}\frac{\lambda_{f\times g \times \widetilde{f\times g}}(n)}{n^s}$ instead.
Sep 13 at 7:10 comment added David Loeffler The quantity you're calling $L(\pi, s)$ looks slightly strange; why do you want to consider this particular series? It is not, as far as I can see, the $L$-function of any automorphic representation (so the notation is a bit misleading, it is not clear what $\pi$ is supposed to refer to). You might perhaps be able to write it as a ratio of automorphic L-functions.
Sep 13 at 4:10 history edited FeiHou CC BY-SA 4.0
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Sep 13 at 1:00 history asked FeiHou CC BY-SA 4.0