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Results tagged with analytic-number-theory
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user 4213
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.
34
votes
Accepted
Shortest/Most elegant proof for $L(1,\chi)\neq 0$
I like the proof by Paul Monsky:
'Simplifying the Proof of Dirichlet's Theorem'
American Mathematical Monthly, Vol. 100 (1993), pp. 861-862.
Naturally this does maintain the distinction between real …
- 20.8k
17
votes
How does one use the Poisson summation formula?
In number theory, the Poisson summation formula is used in proving
functional equations of theta functions (assuring that they are modular forms)
and then via this proving functional equations for zet …
- 8,842
1
vote
What are Mean Values of Ideal Densities in Galois Extensions?
This may be a reference to the the Davenport-Heilbronn theorem
on the distribution of discriminants of number fields.
See
math.stanford.edu/~fthorne/davenport-heilbronn.pdf
for a nice exposition. Str …
- 20.8k