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On pages 516-517 of "Automorphic forms on $GL(2)$", there is a list of expressions contributing to Selberg trace formula.

In (IV), should there be an additional $\frac{1}{2}$ multiple?

In (VII), the function field case, should the upper limit of the integral be $\frac{4 \pi i}{\mathrm{log}\:q}$ (instead of $\frac{2 \pi}{\mathrm{log}\:q}$) and the multiple preceding the integral should be $\frac{1}{4\pi}$ (instead of $\frac{\mathrm{log}\:q}{4\pi}$)?

Is (VII), the number field case correct as written there? Are all the other cases correct? Is there a complete list of mistakes in this book somewhere?

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    $\begingroup$ mathoverflow.net/a/135110/3803 $\endgroup$
    – Peter Humphries
    Commented May 24, 2019 at 10:42
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    $\begingroup$ @PeterHumphries thanks, did not notice that, my bad. I looked up the pdf file, it appears that either my suggestions are wrong, or they are wrong. So it does not completely resolve the question. $\endgroup$
    – user140765
    Commented May 24, 2019 at 10:58
  • $\begingroup$ Have you tried comparing with other presentations of the Selberg trace formula? E.g., Gelbart's book or lecture notes, or Arthur's expositions? $\endgroup$
    – Kimball
    Commented May 24, 2019 at 21:44

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