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Show the trivial zeros for Maass-type L-functions #2828

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davidfarmer opened this issue Mar 21, 2019 · 4 comments
Open

Show the trivial zeros for Maass-type L-functions #2828

davidfarmer opened this issue Mar 21, 2019 · 4 comments
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feature request Feature request L-functions L-functions Maass Maass waveforms
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@davidfarmer
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The plots of L-functions with nonzero imaginary spectral parameters
make it look like RH fails. This is because of the trivial zeros.
A big red dot on the horizontal axis at those points would help people
understand this interesting phenomenon.

Suggested by Dave Roberts.

@davidfarmer davidfarmer added the L-functions L-functions label Mar 21, 2019
@davidfarmer davidfarmer added this to the v1.2 milestone Mar 24, 2019
@davidfarmer
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Refinement:

A red dot when it is Gamma_R(s + i y) and an open red circle when it is GammaR(s + 1 + i y).

In the latter case, the effect on the Z-function is less significant, as can be seen in these examples:
http://beta.lmfdb.org/L/ModularForm/GL2/Q/Maass/4f62419388aece3d9f000016/
http://beta.lmfdb.org/L/ModularForm/GL2/Q/Maass/4f622d0488aece3d9f000003/

If those links stop working because of renaming L-functions, those are the L-functions of
the Maass forms of level 9 and trivial character, with eigenvalue approximately 7.43 .

@AndrewVSutherland AndrewVSutherland added the feature request Feature request label May 18, 2019
@AndrewVSutherland AndrewVSutherland added the Maass Maass waveforms label Jul 23, 2020
@AndrewVSutherland
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Another case noted by John Voight where the Z-plot looks wrong:

https://www.lmfdb.org/L/ModularForm/GL2/Q/Maass/5411a3c1acf7560ce8a6f2b1/

(this is for the Maass form of level 10 with spectral parameter R= 6.4845713681)

@davidfarmer
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On hold until #6235

@davidfarmer
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New cases can be done after #6236

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Labels
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