# The Redheffer Problem

Hi. The Redheffer Matrix is a matrix which is defined as

$R$i,j$=\left\{\begin{matrix}&space;1\mbox{&space;if&space;}i\vert&space;j\mbox{&space;or&space;}j=1\\&space;0\mbox{&space;else}&space;\end{matrix}\right.$.

The Riemann Hypothesis is true iff

$det(R)=O(n^{\frac{1}{2}+\epsilon})$

And this page catalogs all of my attempts to look at this problem. If you wish to contact me, please do so at redheffer at optoutofdatabases dot 33mail dot com . Why am I doing this? Because I got nerd sniped so goddam hard by this problem five years ago that I essentially made my doctorate work useless, destroyed my entire professional career, and now live with my parents doing nothing better with my life than working at a business fixing people's outlook e-mail inboxes, and instead of publishing in journals I now find myself making a site on Neocities. I also managed to estrange everyone I know because I fucked up every personal relationship I have by not being able to shut up about this and sideline every other thing in my life because to hell with having any sort of balance, right? So come along for the ride. I'm pretty confident that it will end with this website turning into something like timecube as I slowly become more deranged, which should hopefully be entertaining to watch.

I should warn you, there's no proof here, very little citations, nor probably any original thoughts or anything worthwhile. With that said--HAVE FUN. What follows is all of the writeups and octave codes that I could muster regarding this project.

This is not formal academics folks. This is a fly-by-the-seat-of-your-pants operation. With that said, below is a blog of my thoughts on the problem that I may update from time to time.

As of my latest writeup, I am convinced more and more that a matrix-approach is not tenable. Given how trivial the process to go from the Redheffer formulation to the Mertens function formulation is, and how I've exhausted nonnegative matrxi factorizations, SSS methods, basic determinant methods, etc.--I'm going to move on to something else for now.

What follows are writeups and codes that I have. You might notice that they're labeled '3' and '7,' respectively. Yes, there are intermediate versions, but there's so much overlap that I thought it would be simpler to just release these two. If you have interest in the intermediate thoughts or my sources, contact me.

2020 Work
• Writeup (pdf warning)
• Relevant Code (Octave warning)

• 2017-2020 Work
• Writeup (pdf warning)
• Relevant Code (Octave warning)