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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.

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 …
Vesselin Dimitrov's user avatar
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 …
Vesselin Dimitrov's user avatar
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 …
Vesselin Dimitrov's user avatar