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Oct 16 '17 at 6:31 comment added Filippo Alberto Edoardo @johnmangual I confess I am a bit lost in your question: when you say " Is there always this link between complex multiplication and the angles of primes?" are you asking for a link between splitting behaviour of primes in $\mathbb{Z}[i]$ and $a_p$ being $0$? This is the theory of Complex Multiplication, i.e. class field theory for imaginary quadratic fields. Or am I missing your point?
Oct 16 '17 at 0:22 comment added David Lampert Find this enjoyable talk by Serre
Oct 15 '17 at 22:59 comment added john mangual @FilippoAlbertoEdoardo In Rudnick-Waxman, there's no discussion of Elliptic curves. They don't use it at all. That's why Chen's blog was such a surprise. Yet, they do use some kind of analogy to random matrices.
Oct 15 '17 at 22:36 comment added john mangual is there a higher-rank analogue complex multiplication of the splitting of the primes? what do you think is happening in the non-CM case?
Oct 15 '17 at 22:11 comment added Filippo Alberto Edoardo Hi Geordie, are you aware of the recent preprint arxiv.org/pdf/1705.07498.pdf where Rudnick and Waxman discuss a great deal of this?
Oct 15 '17 at 21:40 comment added Geordie Williamson Do you know anywhere where the implications of this beautiful general conjecture is spelled out in the case of complex multiplication? It must be somewhere, but I (and perhaps the OP?) don't know the literature well.
Oct 15 '17 at 21:09 history answered Watson Ladd CC BY-SA 3.0