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This is a very soft question, but it is somewhat relevant to some other questions, like Which are the best mathematics journals, and what are the differences between them?.

I've read that Notices AMS provides annual (at least) stats on backlogs, turn-around times and so on (when is this, by the way - is it the same month each year? And where is it? The faultless google has let me down ;_;) But what are some of the quickest journals? That being said, one has to balance speed with length of allowed papers (having a page limit of 15 sure would help speed up refereeing times, or am I optimistic?), general reputation and level of specialisation.

What is the quickest journal you are aware of for 'general' papers? For papers in your special field?

Alternatively, what about (unreasonably?) slow turnaround? I'm not asking for anecdotes, but documented evidence (Edit: perhaps documented evidence is too strong. I just don't want 'My paper took 3 years because it sat in someone's spam filter and then got lost and then the referee forgot about it'. If you have anecdotal evidence, then it should be either 'common knowledge' or at least corroborated by people you know). If this slow journal is because it accepts top-level research papers that are over 100 pages in length, then please say so.

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I am a bit short on the evidence that you're after, but thought I'd remark that some of the quickest response times I've had has been followed by what, to me at least, seemed quite shoddy post-acceptance-processing. This is to do with the publisher's apparent workflow rather than the journal, of course. – Yemon Choi Feb 21 '11 at 1:55
Where did you read that this is information is published in the Notices of the AMS? I don't remember every hearing about anything like that. – Ben Webster Feb 21 '11 at 2:09
@Ben - In the book 'A primer of mathematical writing' (page 82/83 on google books). See the link in the answer by Jason Rute below. – David Roberts Feb 21 '11 at 3:14
I am a little worried that the journals which appear as answers to this question would become slower... – Hailong Dao Feb 21 '11 at 6:20
That is a good point. But I would hope that careful consideration of the appropriateness of the journal, its editors and target audience would outweigh the rush by people to see their articles appear quicker. There are constraints at least for Australian mathematicians as to the rankings of journals as seen by our main funding agency which are a huge factor in deciding where to publish. – David Roberts Feb 21 '11 at 6:41

International Math Research Notices is a journal that accepts `general' papers and has a reputation for turning papers around quickly. It is in fact part of their mission statement to do so.

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When IMRN first started, they were breathtakingly fast. I published an article in one of the first issues, and I think it took like two weeks from start to end. This was before the internet, so I remember getting proofs by Fedex from Hong Kong. – Deane Yang Feb 21 '11 at 3:09
Wow! Really before the internet? (tongue removed from cheek) Was it the paper "Existence and regularity of energy-minimizing Riemannian metrics", Int Math Res Notices (1991) Vol. 1991 7-13? – David Roberts Feb 21 '11 at 3:22
OK. Maybe I exaggerated. We old guys often do. – Deane Yang Feb 21 '11 at 4:33

I Googled "AMS journal backlog" and found this.

I'm not sure about the other questions.

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Ah, there it is. – David Roberts Feb 21 '11 at 1:49

Mathematical Research Letters generally asks referee reports to be returned within a month I think. It is also ``dedicated to rapid publication of short complete papers of original research in all areas of mathematics.'' It does ask that papers be less than 20 pages though...

However, based on the data in Jason Rute's answer, they don't seem to be super fast...

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