At the MathoverFlow International Mathematics Forum, Xu Chuan's paper on the arxiv preprint website can be said to be the most discussed topic in the past two days.

However, a slight difference from previous situations is that there are almost no top mathematicians in the crowd participating in the discussion.

Although the vast majority of mathematicians are relatively 'cold', especially many older generation mathematicians, not to mention surfing the Internet, even mobile phones and computers are not often used.

But in any case, when faced with such a major topic as the millennium problem, and the publication of the paper is still semi-recognized as the first person in the mathematical community today, many top mathematicians in the past will basically stand up and express it.

However, this time, the top bulls in the entire mathematical community seemed to have collectively lost their voices, and there was almost no movement.

Even Professor Tao Zhexuan, a 'surfing assistant' who used to love to express his views on the Internet, did not appear this time, nor did he update his blog and Twitter.

This strange situation has also attracted a lot of discussion and attention on major mathematical forums and websites.

After the restoration of arxiv, most of the people who paid attention to this matter also downloaded the paper, whether they could read it or not, at least they still had to 'install' it on the Internet.

[Anyway, what happened to Professor Xu's paper?] Can you give me an accurate word? 】

[Professor Tao has not come out, and there is no information so far. 】

[Wait, the millennial problem is not a proof paper of this level, and it will not be determined in a moment. Professor Tao didn't come out, maybe he was reading the paper, and my friend is from the University of California, and he said that Professor Tao had already pushed off the next week's classes. 】

[Professor Xu's paper published on arxiv downloaded and read, this paper does not seem to have anything to do with the Riemann hypothesis, and I did not see any research ideas about the critical zone in it. 】

[Upstairs is pretending to understand, and the direction of Xu's thesis research is the Riemann conjecture. 】

[I also read Professor Xu's paper, and it seems that he did not follow the critical zone research method, but opened up another new path, regressing the Riemannian function to the π(x) prime number counting function, and then conducting equivalence research. 】

【？？ Abandoning the idea of critical zone research? Does he feel that this path is not going to work? 】

【Impossible!】 Critical band compression is currently the best way to advance the Riemann conjecture, and the idea of regression to the π (x) prime number counting function I know has been studied a long time ago, but it doesn't work at all, and the difficulty is greater than the critical band idea! 】

Who knows? They may or may not have their own ideas. 】

The discussion at the MathoverFlow International Mathematics Forum was very lively.

Some people think that many mathematicians have not come out to speak out, which is undoubtedly not optimistic about Professor Xu's paper.

On the other hand, some people stand on the side of support, believing that Professor Xu's published papers have basically been strictly confirmed in his usual practice, and they will not be published without 100% certainty.

This part is quite a lot, after all, over the years, Xu Chuan's good academic reputation has brought him many fans.

Of course, more people are silently eating melons and waiting for news.

After all, it's only been a few days?

The verification of this millennial math puzzle is measured in months, or even years.

At a time when discussions are raging in major mathematics forums and online, as well as in major mathematics institutions or universities, a brand new paper has been quietly published on the ARXIV preprint website.

"For each set of Janssen polynomials with the same "degree", except for the offset 0+N≤δ(X)≤1-1/2· N, the rest all meet the requirements of the Riemann conjecture! 》

This is the title of the paper, and it is also a brand new achievement that Xu Chuan has made these days.

And this title is the answer he got by shrinking the Riemann function ζ back to Jensen's inequality, and then studying it through sub-sigma algebra.

In 1927, Polya proved that the Riemann conjecture, a conjecture about the zero-point distribution of Riemann ζ functions, is equivalent to proving the zero-point distribution of another type of function—in other words, as long as certain properties of the zero-point distribution of that other type of function are demonstrated, it is equivalent to proving the Riemann conjecture.

To put it simply, the Riemann conjecture can be studied by using the Jamssen polynomial associated with the Riemann ζ function.

As long as the shift and zero point of the Jensen polynomial are extended, the same result can be obtained as the zero distribution of the Riemann ζ function.

Jinling, at the foot of the Purple Mountain.

Xu Chuan, who hadn't seen much of the sun for more than a month, walked out of the villa.

The weather is still hot in mid to early October, but with the Purple Mountain in the background, the temperature at the foot of the mountain is not so hot that people can't even get out.

At the door of the courtyard, the unique Hongqi car waited quietly.

"Professor, where are you going?"

Pulling the car door, Xu Chuan got into the car and replied casually: "Let's go to the Chuanhai Materials Research Institute first." ”

If it weren't for Senior Brother Fan Pengyue who had been constantly reporting information to him, to be honest, he would have almost forgotten that there was a materials research institute under his name.

This time, it is also because Brother Fan reported the latest research progress in the direction of batteries, and with the efforts of the lithium battery minister of the Institute for four years, the lithium-sulfur battery has finally made a new breakthrough.

This news was passed on by Senior Brother Fan Pengyue two days ago, but at that time he was perfecting the final steps of the weak Riemann conjecture thesis, so he ignored it.

Now, now that the paper has been uploaded to the ARXIV preprint website, he finally has time to visit the Chuanhai Institute of Materials Research to see what is going on.

To be honest, lithium-sulfur battery technology has not broken through until now, which is a bit slow in Xu Chuan's opinion.

After all, as early as four or five years ago, he led the team in the Chuanhai Materials Research Institute to successfully develop artificial SEI films.

This achievement directly solves the problem of the generation of lithium dendrites in lithium batteries, and the registered major has also brought him billions of funds.

The emergence of artificial SEI films has also triggered changes in the lithium battery industry, and it can be said that countless enterprises or groups have flocked to this field.

Although there are only two types of lithium batteries as a whole, 'lithium metal batteries' and 'lithium-ion batteries', in fact, they can be split into many series and types.

For example, the most common lithium-ion batteries generally use lithium alloy metal oxide as the cathode material, graphite as the anode material, and non-aqueous electrolyte as the battery.

According to the different metal materials of cathode lithium alloy, lithium cobalt oxide batteries, lithium manganese oxide batteries, lithium nickel oxide batteries, and lithium iron phosphate batteries can be separated. And so on and so forth.

Batteries are an unusually large market, from mobile phones, computers, various electronic products, to aerospace and other top fields, it can be said that none of them can leave the battery.

With such a huge market cake, a capitalist who does not want to come in and take a bite is not a qualified capitalist.

Four or five years have passed, and on the basis of artificial SEI films, countless different models and types of lithium batteries have been extended all over the world.

Even the capacity and battery life of some lithium batteries have already exceeded the 'carboxymethyl cellulose-lithium fluorocarbon' lithium battery developed by Xu Chuan himself.

This has also led to the Chuanhai Materials Research Institute, which was famous in the field of batteries at the beginning, and now it has come to an end.

If it weren't for the fact that no one could shake the core artificial SEI film for the time being, and the high-temperature superconducting materials still supported its business, it is estimated that its existence would be like a meteor crossing the atmosphere, shining for a while, and then ending in glory.

Of course, this is also related to Xu Chuan's failure to focus his research and energy on Chuanhai materials research.

For this research institute established a few years ago, except for leading the team to complete artificial SEI thin film technology and high-temperature copper-carbon-silver composite superconducting materials, he has hardly cared about other things.

However, let go and let go, the general research direction of Chuanhai Materials Research Institute has always been formulated by him.

For example, the lithium-sulfur battery technology that broke through this breakthrough, the lithium-air battery that is still being developed in the laboratory, the research and development of superconducting materials, and a series of technologies such as carbon dioxide synthesis starch and carbon compounds are all the directions he personally specified.

It's just that these technological breakthroughs may take a bit longer than he imagined and planned.

Originally, Xu Chuan thought that after the completion of artificial SEI thin film technology, the lithium-sulfur battery would be completed in two or three years at the latest.

As a result, it has been four or five years now, and there have been some changes.

If only one laboratory of the Chuanhai Materials Research Institute is researching this, four or five years is nothing.

Now it is the battery industry all over the world, and it can be said that almost all those who have investment will study lithium-sulfur batteries and lithium-air batteries, after all, lithium-sulfur batteries and lithium-air batteries are the phased development steps of lithium-ion batteries.

As a result, in the past four or five years, the whole world has not heard of a company that has made a breakthrough in this field.

In the field of lithium battery research, major laboratories and enterprises are much slower than Xu Chuan imagined.

At the same time, when Xu Chuan rushed towards the Chuanhai Materials Research Institute, it was not surprising that the topic related to the Riemann conjecture was detonated again.

Less than half an hour after Xu Chuan dropped the proof paper of the weak Riemann conjecture onto Arxiv, mathematicians around the world once again turned their attention to this preprint website.

Fortunately, Los Alamos National Laboratory, which is responsible for managing and maintaining the website, reacted immediately and added all the spare servers, which barely maintained the swarming traffic, so that many scholars could see the relevant papers in the first time.

At the same time, at the MathoverFlow International Mathematical Forum, the voices of discussion hit like a tsunami.

【arxiv！ Professor Xu! Proof of the weak Riemann conjecture! 】

[Huh? 】

[God! Unbelievable, it's only been a few days?! 】

[Judging from the time he uploaded it before, the proof of this weak Riemann conjecture is less than a week between the two!] Only six days and nine hours to be exact! 】

【Hiss~! That's too fast, right? 】

[Isn't it? Didn't Professor Xu upload the paper to ARXIV to study Jensen's polynomials and π(x) prime counting functions? 】

[I suggest you study math well before coming here.] 】

[The Jensen polynomial is named after the Danish mathematician Jensen's study of it, and it has the same zero-point distribution property as the Riemann conjecture, that is, the zeros of the Jensen polynomial are all real numbers. In other words, as long as you can prove that the zero point of the Jensen polynomial is all real numbers, you have also proved the Riemann conjecture! 】

[If I'm not mistaken, this equivalence proposition seems to have been more difficult to deal with for a long time than even the Riemann conjecture itself.] 】

[Yes, because there are infinitely many sets of Jensen polynomials—distinguished by so-called "degrees", and each group of infinitely many - distinguished from each other by so-called "offsets", it is probably more difficult to solve them on the present basis than the Riemann hypothesis.] 】

[At least the Riemann conjecture has a way to prove the critical band contraction method, and it has also advanced it to No(T)>0.4N(T).] 】

On the MathoverFlow math forum, the discussion was extremely intense.

However, most of the discussion focused on the proof that Xu Chuan was able to complete the weak Riemann conjecture so quickly, and the route and direction he studied.

As for the correctness of the paper itself, not many people have discussed and studied it.

After all, after the emergence of the proof paper of the weak Riemann conjecture, the scholars who still have time to surf the Internet are basically the 'scumbags' who can't read the papers.

Those who can understand the paper are basically immersed in the paper at the moment.

On the other side, in a villa not far from the University of California, Los Angeles, California.

Tao Zhexuan, who was immersed in using the tools created by Xu Chuan to study Riemann's conjecture, was suddenly woken up by a ringtone of his mobile phone.

Frowning, he picked up the phone from the desk next to him, it was his assistant calling, his finger slid across the screen, and he answered the call.

"Wyatt, didn't I say there's nothing to bother me?"

On the other side, the female assistant's voice was quickly transmitted.

"I'm sorry, Professor Tao, but that's what you ordered. On arxiv, the professor Xu you got my eye on uploaded a new paper. ”

Hearing this, Tao Zhexuan was stunned for a moment, his breathing was also shortness of two minutes, and he quickly asked with a hint of luck: "Professor Xu's thesis, what is it?" ”

"In terms of the Riemann conjecture, judging by the title of the paper, it seems to be a proof paper of the weak Riemann conjecture."

Hearing this, Tao Zhexuan was silent for a while, then threw away the pen in his hand, fell to the back of the chair, and silently stared at the primary color wooden door not far away.

Just when the female assistant almost thought that the phone was hung up, Tao Zhexuan spoke: "Transfer the paper to my mailbox." ”

"Okay, Professor"

Hanging up the phone, Tao Zhexuan stared at the ceiling of the study silently for a long time, with a hint of complexity on his face.

He had thought he was fast enough, and that this week, using that tool and paper to continue researching the breakthrough against the Riemann hypothesis, had already yielded some results.

It can even be said that he has already seen the figure of the weak Riemann conjecture, and if he is given another month, maybe he will be able to solve this problem.

However, in just one week, the man had already solved the weak Riemann hypothesis.