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I want to publish a paper in a math journal. I want to know the list of top journals which have the shortest review time.

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    $\begingroup$ There's unfortunately no such list (on what could it be based? the journals' submission information is not public). The review time depends not only on the editorial board but on the referees; for a single journal at a given time the review time is highly variable. Another parameter: top journals are likely to ask short reports before the full process (more and more journal do this now). Also, needless to say, about defining "review time": the rejection time is in average shorter than acceptance time. So undoubtly the shortest review time is achieved by universalrejection.org $\endgroup$
    – YCor
    Commented Jan 27, 2022 at 9:03
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    $\begingroup$ The very top journals actually tend to have rather longish review times for papers they accept, because the papers are substantial and important, and so the referees seem to take a more thorough approach, from what I understand. If you need your work out quick, then a preprint 8s a better option. $\endgroup$
    – David Roberts
    Commented Jan 27, 2022 at 10:00
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    $\begingroup$ Looking at your other questions on math.SE, I'm not convinced that you will find the top journals to be what you think them to be. $\endgroup$
    – David Roberts
    Commented Jan 27, 2022 at 10:20

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The Notices of the American Mathematical Society publishes such a list once a year.
Well, strictly speaking, it is not "review time" but time from submission to publication.
Look in the table of contents for the word "backlog".

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