09/23/2013, 09:14 PM
This is an old thread but still I felt the need to comment.
The paper of Kouznetsov did not get as popular as some here expected , but I - as a skeptic - did.
One of the reasons might be this :
INTEGRAL TRANSFORMS HAVE CONDITIONS !
A good example is the Mellin inversion theorem.
Those conditions can be quite complex.
If an equation involved unknown functions AND integral transforms , it is a bit handwaving to assume all the conditions are met + uniqueness AND existance.
From my experience in number theory , many of my " unpublished wrong crank ideas " were mistakes by assuming conditions of integral transforms holds.
One could easily prove RH , collatz and Hardy-Littlewood I or II with those silly integrals , that turn out not to be valid in some sense ( conditions not met , some formula's not valid , divergence , summability method fail/dubious , using assumptions equivalent to the whole conjecture , assuming differentiability , ... )
Most pro mathematicians see this immediately.
I am unaware of any paper that adresses these issues , and I assume nobody is willing to pay for it before being convinced.
You see , tetration is not mainstraim , so the access should be easy and the burden of proof is on the claimer side.
Don't get me wrong , I like Kouznetsov and some of his ideas.
But those are my viewpoints , and by the lack of popularity of his paper ( in retrospect years later ) I assume it is the view of most.
regards
tommy1729
The paper of Kouznetsov did not get as popular as some here expected , but I - as a skeptic - did.
One of the reasons might be this :
INTEGRAL TRANSFORMS HAVE CONDITIONS !
A good example is the Mellin inversion theorem.
Those conditions can be quite complex.
If an equation involved unknown functions AND integral transforms , it is a bit handwaving to assume all the conditions are met + uniqueness AND existance.
From my experience in number theory , many of my " unpublished wrong crank ideas " were mistakes by assuming conditions of integral transforms holds.
One could easily prove RH , collatz and Hardy-Littlewood I or II with those silly integrals , that turn out not to be valid in some sense ( conditions not met , some formula's not valid , divergence , summability method fail/dubious , using assumptions equivalent to the whole conjecture , assuming differentiability , ... )
Most pro mathematicians see this immediately.
I am unaware of any paper that adresses these issues , and I assume nobody is willing to pay for it before being convinced.
You see , tetration is not mainstraim , so the access should be easy and the burden of proof is on the claimer side.
Don't get me wrong , I like Kouznetsov and some of his ideas.
But those are my viewpoints , and by the lack of popularity of his paper ( in retrospect years later ) I assume it is the view of most.
regards
tommy1729