Timeline for On the class number

5 events

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Feb 10, 2012 at 0:58	comment	added	Guillermo Mantilla		@Frank: OK, after seeing the results by Soundararajan, mentioned in the comments above, I see your point.
Feb 10, 2012 at 0:54	comment	added	Noam D. Elkies		Since typically $h(d)$ is of size about $d^{1/2}$, a naïve probabilistic heuristic suggests that each $h$ should arise about $h$ times. There are confounding factors, most notably coming from genus theory which gives a lower bound on the 2-valuation of $h$; e.g. odd $h$ should be particularly rare because they arise only when $d$ is prime. But that's a $\log h$ effect so surjectivity should still hold once it's been checked out to say $h=10^4$ by exhaustive computation. As with the Goldbach conjecture, though, the expected existence of numerous preimages doesn't mean a proof is forthcoming.
Feb 10, 2012 at 0:47	comment	added	Guillermo Mantilla		Hi Frank! "although it is widely expected to be" really? it might be ignorance of my part, but I've never heard this before. In fact, I'm more inclined to guess that $f$ is non surjective.
Feb 10, 2012 at 0:33	history	edited	Frank Thorne	CC BY-SA 3.0	deleted 10 characters in body
Feb 10, 2012 at 0:25	history	answered	Frank Thorne	CC BY-SA 3.0