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I did a little search about available literature on gaps between primes, and, although I was confident in thinking that books about that topic are very rare, I really wasn´t sure that I will find exactly not a single one?

I found an article by Zhang, of which I knew before, but although I knew that really not much is known about that topic, I expected that there is at least one book in which all the rigorous results about gaps are collected.

So, because that topic interests me, what would you suggest me to read, I mean, which book would be appropriate as at least prerequisite to learn more about that topic?

Also, I am really not skilled enough in intersections of number theory with complex-variable functions theory, so I would more like some recommendations of number theory books that have much more algebraic than analytic flavour.

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    $\begingroup$ The authoritative text that gives the necessary background to understand the best results on gaps between primes, especially those of Zhang and Maynard, is the book Opera de Cribro by Henryk Iwaniec and John Friedlander. $\endgroup$
    – Stanley Yao Xiao
    Commented Nov 7, 2019 at 18:27
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    $\begingroup$ Most of the recent work is available on ArXiv or on blogs. I am not aware of books focusing on prime gaps. Terry Tao's blog is a good place to start, and James Maynard posted a recent survey article. Gerhard "Would Like To Fill Gaps" Paseman, 2019.11.07. $\endgroup$
    – Gerhard Paseman
    Commented Nov 7, 2019 at 18:28
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    $\begingroup$ You can also see Kevin Ford's notes faculty.math.illinois.edu/~ford/sieve_methods_Sp2015.html $\endgroup$
    – George Shakan
    Commented Nov 7, 2019 at 18:44
  • $\begingroup$ @StanleyYaoXiao When I saw description of that book I thought that I could just let professionals do their job and I could purchase Closing the Gap: The Quest to Understand Prime Numbers for myself. $\endgroup$
    – user147968
    Commented Nov 7, 2019 at 18:46
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    $\begingroup$ The analysis in the prime gaps work mostly has little to do with functions of a complex variable. $\endgroup$
    – Will Sawin
    Commented Nov 7, 2019 at 18:55

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