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Results tagged with nt.number-theory
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user 21933
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
6
votes
2
answers
893
views
why Riemann Hypothesis over curves is easy but 'normal' hypothesis for the Riemann Zeta func...
despite both zetas $ \zeta (s,X) $ and $ \zeta (s)$ have the same functional equation, the same Euler prodcut and the same Riemann-Weil formula
why one of them is 'easy' and can be solved but the ot …
- 41
5
votes
1
answer
371
views
Trace over the zeros with real part 1/2 Only
If RH is not true, we have that Weil's explicit formula still holds:
$$ \sum_{\gamma} h(\gamma) = h(i/2)+h(-i/2)-2 \sum_{n=1}^{\infty} \frac{ \Lambda(n)}{ \sqrt n}g(logn)+\frac{1}{2\pi} \int_{-\infty …
- 41
1
vote
0
answers
585
views
How ..did Connes get it (trace formula)
i have been reading or at least trying to understand how Connes get the density (approximate) of states
$ N(E)= \frac{E}{2\pi}log \frac{E}{2\pi}- \frac{E}{2\pi}+ \frac{7}{8}+ \frac{1}{\pi}arg \zeta(1 …
- 41