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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

47 votes
3 answers
5k views

Class Numbers and 163

This is a bit fluffier of a question than I usually aim for, so apologies in advance if this doesn't pass the smell test for suitability. Likely my favorite fun fact in all of number theory is the jux …
Cam McLeman's user avatar
  • 8,467
13 votes
Accepted

Most squares in the first half-interval

Nope! Amazingly enough, no elementary proof of this fact is yet known (Edit: See KConrad's answer). The difficulty is tied up in some pretty fantastic algebraic/analytic number theory, namely the a …
Cam McLeman's user avatar
  • 8,467
5 votes
Accepted

Injectivity of Transfer (Verlagerung) map

I'm not sure how to answer the more philosophical question (it's likely you could encode enough of the axioms to force the purely group-theoretic version of the question to be true, but to ask whether …
Cam McLeman's user avatar
  • 8,467