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L-ratios for Bianchi newforms #6288

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JohnCremona opened this issue Dec 5, 2024 · 0 comments
Open

L-ratios for Bianchi newforms #6288

JohnCremona opened this issue Dec 5, 2024 · 0 comments
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@JohnCremona
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The bmf_forms table has a column L-ratio which is supposed to hold the rational value (computed exactly) L(F,1)/Period(F). There are several issues:

  • A glitch in the template code logic means that when the stored value is 0 (which will be true whenever the analytic rank is positive), the value is not displayed at all, instead of showing 0.
  • The knowl on "L-ratio" is mf.bianchi.anr (analytic rank) which is wrong. There is no knowl for the L-ratio, and there should be.
  • Lewis Combes tells me that he thinks some of these ratios are wrong, so I need to check my code and then recompute them.

In view of this I propose to hide the L-ratio display right away, pending a fix of the data. Then, when the data is fixed (and Lewis and I agree) I can redisplay the values and put in a knowl.

By the way, it is hard to compare this ratio with the similar number for elliptic curves (of rank 0) as predicted by the BSD, since it is not isogeny-invariant and there is no way of singling out the "right" curve in the isogeny class which has a matching ratio. I wrote a paper about this long ago, which included examples where more than one curve had the right ratio.

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