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Results tagged with analytic-number-theory
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user 6153
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.
1
vote
Kronecker's Jugendtraum for real quadratic fields?
Hecke started on this area a century ago https://en.wikipedia.org/wiki/Hilbert's_twelfth_problem. As far as I know his ideas have not been taken much further.
- 12.6k
7
votes
How should an analytic number theorist look at Bessel functions?
From the point of view of analytic number theory, the point usually would be asymptotic behaviour. This is typically well understood, and is in the massive book of Watson. Apart from that, yes, numero …
- 12.6k
12
votes
Approaches to Riemann hypothesis using methods outside number theory
I think, tautologously, any method proving the Riemann Hypothesis (or even seriously improving our knowledge on the zeroes) becomes "number theory" immediately. That said, I know what the question mea …
- 12.6k
4
votes
Accepted
Dirichlet's Divisor Function
Use Wikipedia: http://en.wikipedia.org/wiki/Dirichlet_divisor_problem .
- 12.6k
7
votes
How does one use the Poisson summation formula?
Probably different answers in harmonic analysis and number theory.
Place a Dirac measure at each of the integers and you get a distribution that is close to being self-dual under the Fourier transfor …
- 12.6k