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Results tagged with riemann-hypothesis
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user 26522
Questions about the famous conjecture from Riemann saying that the non-trivial zeroes of the Riemann Zeta function all lie on the so-called critical line $\Re(s)=\dfrac{1}{2}$, its various generalizations and the different approaches towards its solution.
6
votes
Accepted
Lexicographic distribution of irreducible polynomials
This is true.
By Gauss's theorem (the inclusion-exclusion formula for the number of irreducibles of a given degree), we may restrict to polynomials of a fixed degree $r$. A moment of reflection then …
- 13.8k
9
votes
1
answer
493
views
Subspaces of $L^2(0,1)$ dense on every truncation $L^2(c,1)$
It may be better to move this to a separate question.
Let me call a linear subspace $V \subset L^2(0,1)$ to be tame if, for every linear subspace $W \subset V$, either $W$ is dense in $L^2(0,1)$, or …
- 13.8k
10
votes
1
answer
581
views
Are the polynomials in $\{1/t\}$ dense in $L^2(0,1)$?
Added. My question in the title was solved (in the negative) by Nik Weaver (in the answer below) and Mateusz Kwaśnicki (in the comments). In both solutions, the reason is that the $L^2$ density fails …
- 13.8k