A Possible Proof Of The Riemann Hypothesis

PLEASE DON'T DOWNLOAD THIS,GO TO THE LAST VERSION INSTEADLast version as I write this: 104 My last version when I write this is 103, Version 100 is the right one. Please refer to Version 100. The constraints I thought were not satisfied were actually satisfied. All the x_k must be real so all the $\Delta_{n-k}$ must be positive. Nothing to see. All the constraints I relied on proved to be loose. I need more refinement. In the part with the quadratic equations which I relied on, with the constraint on $r_n$ as the quadratic coefficient $f_{n-k-1}$ of the new $\Delta_{n-k}$ got negative (to require the following $\Delta_{n-k-1} \ge 0$), I figured out that this constraint on $r_n$ was valid only up to a certain point; and to figure out this $k$ up to which the constraint holds, I had to express $r_n=\frac{\sum_{k=1}^{n} \frac{1}{k^{2a_n}}}{\sum_{k=1}^{n} \frac{1}{k^{2a_n}}-\left(\sum_{k=1}^{n}\right)^2}$ which in the end made the quadratic equations obsolete. Because I would anyway have to express $r_n$ this latter way. In my previous versions, I really didn't pay attention to the $k$ up to which we needed the $\Delta_{n-k}$ positive. I assumed we needed all of them positive. Which is false, when the quadratic coefficient of one of them got positive it just broke the chain of constraints. In the present study, even the $a_{+\infty} < \frac{1}{2}$ doesn't hold, I rushed while replacing with the asymptotic equivalence, we actually end up with 0=0 here as well. What was very vile with that approach with the quadratic equations is that it seemed to make so much sense, with the $1-2a_n$ appearing here and there, but didn't make any in the end. I feel dumb now. Thank you all for you attention. I am sorry. I am currently figuring out new constraints, I keep you updated whenever I can. We may even get back our beloved chain of quadratic equations. This file is somehow useless, download it if you want but know it's erroneous.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-02-04
DOI
https://doi.org/10.5281/zenodo.14799143
Primary Topic
History and Theory of Mathematics
Type
article
Field-Weighted Citation Impact
0.00
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article

A Possible Proof Of The Riemann Hypothesis

Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
article

A Possible Proof Of The Riemann Hypothesis

article en

Abstract

PLEASE DON'T DOWNLOAD THIS,GO TO THE LAST VERSION INSTEADLast version as I write this: 104 My last version when I write this is 103, Version 100 is the right one. Please refer to Version 100. The constraints I thought were not satisfied were actually satisfied. All the x_k must be real so all the $\Delta_{n-k}$ must be positive. Nothing to see. All the constraints I relied on proved to be loose. I need more refinement. In the part with the quadratic equations which I relied on, with the constraint on $r_n$ as the quadratic coefficient $f_{n-k-1}$ of the new $\Delta_{n-k}$ got negative (to require the following $\Delta_{n-k-1} \ge 0$), I figured out that this constraint on $r_n$ was valid only up to a certain point; and to figure out this $k$ up to which the constraint holds, I had to express $r_n=\frac{\sum_{k=1}^{n} \frac{1}{k^{2a_n}}}{\sum_{k=1}^{n} \frac{1}{k^{2a_n}}-\left(\sum_{k=1}^{n}\right)^2}$ which in the end made the quadratic equations obsolete. Because I would anyway have to express $r_n$ this latter way. In my previous versions, I really didn't pay attention to the $k$ up to which we needed the $\Delta_{n-k}$ positive. I assumed we needed all of them positive. Which is false, when the quadratic coefficient of one of them got positive it just broke the chain of constraints. In the present study, even the $a_{+\infty} < \frac{1}{2}$ doesn't hold, I rushed while replacing with the asymptotic equivalence, we actually end up with 0=0 here as well. What was very vile with that approach with the quadratic equations is that it seemed to make so much sense, with the $1-2a_n$ appearing here and there, but didn't make any in the end. I feel dumb now. Thank you all for you attention. I am sorry. I am currently figuring out new constraints, I keep you updated whenever I can. We may even get back our beloved chain of quadratic equations. This file is somehow useless, download it if you want but know it's erroneous.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 55%
History and Theory of Mathematics
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