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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.
2
votes
Lower bounds for split primes in Real quadratic fields
This is a bit of a follow up to Franz's answer, but is also a bit different.
Dirichlet's class number formula tells us that $$hR = \frac{\mu(K)\sqrt{|D|}}{2^r(2\pi)^s}L(1,\chi)$$
A particular case o …
2
votes
Accepted
Calculating the infinite product from the Hardy-Littlewood Conjecture F
This problem was studied by a few, and the ideas involve too much latex to write here. Mainly there are ideas of transforming to crazy weighted sums and then use ERH to bound errors from crazier integ …