I just read the description of this book and wondered about the sentence:

additive structure is needed for proving the Riemann hypothesis

that is based on an example by H. L. Montgomery et. al.

Can someone explain what this sentence means, that is, how additive structure is reflected in the Riemann hypothesis?

N.b: If you think the question is too vague (I can't be more precise because I have no clue on what it means, but would like to get some idea) or it doesn't belong to MO because it doesn't address a concrete mathematical problem, please feel free to vote to close.

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    $\begingroup$ One obvious point is that Beurling systems satisfy a PNT, but not necessarily a RH. Thanks, by the way, for notifying of this very interesting future publication. $\endgroup$ Sep 3 '16 at 0:41
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    $\begingroup$ I suspect Vesselin Dimitrov is right. I think the paper of Montgomery being referenced in the AMS description may be `Beurling primes with large oscillation' by Diamond, Montgomery, and Vorhauer (link.springer.com/article/10.1007/s00208-005-0638-2) $\endgroup$ Sep 3 '16 at 4:26

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