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I like Lagarias "elementary" reformulation of Robin's theorem: that RH is true iff

$\sigma(n)\leq H_n+e^{H_n}\log(H_n)$

holds for every $n\geq 1$, where $\sigma(n)$ is the sum of divisors function and $H_n$ is the nth harmonic number.

It's major appeal is that anyone with rudimentary exposure to number theory can play with it. Having spent the better part of my youth fiddling with this reformulation really brang brought out the enormous difficulty of proving RH. In a way I think this reformulation is evil, because it looks tractable, but is ultimately useless and perhaps even harder to work with than other more complex reformulations. On the other hand I hope a future proof of RH will involve this reformulation because then I might have a chance of understanding the proof!
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I like Lagarias "elementary" reformulation of Robin's theorem: that RH is true iff

$\sigma(n)\leq H_n+e^{H_n}\log(H_n)$

holds for every $n\geq 1$, where $\sigma(n)$ is the sum of divisors function and $H_n$ is the nth harmonic number.

It's major appeal is that anyone with rudimentary exposure to number theory can play with it. Having spent the better part of my youth fiddling with this reformulation really brang out the enormous difficulty of proving RH. In a way I think this reformulation is evil, because it looks tractable, but is ultimately useless and perhaps even harder to work with than other more complex reformulations. In particular it On the other hand I hope a future proof of RH will involve this reformulation because then I might have a chance of understanding the proof!
show/hide this revision's text 2 added 15 characters in body

I like Lagarais Lagarias "elementary" reformulation of Robin's theorem: that RH is true iff

$\sigma(n)\leq H_n+e^{H_n}\log(H_n)$

holds for every $n\geq 1$, where $\sigma(n)$ is the sum of divisors function and $H_n$ is the nth harmonic number.

It's major appeal is that anyone with rudimentary exposure to number theory can play with it. Having spent the better part of my youth fiddling with this reformulation really brang out the enormous difficulty of proving RH. In a way I think this reformulation is evil, because it looks tractable, but is ultimately useless and perhaps even harder to work with than other more complex reformulations. In particular it On the other hand I hope a future proof of RH will involve this reformulation because then I might have a chance of understanding the proof!. proof!
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