The top student must be diligent

Maynard said: "I think I should give my share to Xiao Yi. I really didn't play a big role."

At this time, although the agreement has not been completed, they have already started to discuss how to divide the 10 million US dollars.

Of course, this is also because after the two most critical problems have been solved, they have become very confident in getting the 10 million US dollars.

Which other group has come up with a protocol that can not only prevent the trading platform from stealing, but also avoid hacker intrusions like theirs?

Hearing the conversation of the three professors, Xiao Yi was at a loss whether to laugh or cry, and quickly waved his hand and said: "No, no, there are other parts of the entire agreement that have not been completed. If I were alone, I would definitely not be able to complete them all, not to mention that they need to be programmed."

"..."

After a discussion like this, they finally made a decision. Xiao Yi took 6 million US dollars, and the remaining 4 million was distributed to Terence Tao and others according to their respective contributions.

For example, programming is the work of Terence Tao and Kleinrock, and some other mathematical work will be completed by James Maynard.

As for Xiao Yi, he didn't have to do anything next.

After solving these two most troublesome problems, if he also did other things, wouldn't others feel embarrassed when it came time to divide the money?

In the end, it might even lead to a worse relationship.

Xiao Yi, who understood this, of course, did not continue to take on too much responsibility and no longer cared about this matter, but did his own thing.

He naturally had his own things to do.

The first thing was to sort out his paper [Xiao's Polynomial Expansion].

As a new mathematical method, and he independently developed it, it was naturally to be published separately.

As for whether they need to worry about being learned by their competitors, there is no need to worry.

After all, it takes time for those people in the computer industry to understand this paper.

To be more conservative, even if they really understand this paper, it is still a problem whether they can immediately associate it with defense against classification sieve attacks, not to mention the technical difficulties.

Perhaps in this world, only Xiao Yi can think of it to solve the problem of classification sieve based on it.

…

“Hmm…I heard from Terence Tao that this thing can also be used to study the Riemann hypothesis?”

While sorting out the paper, Xiao Yi thought about it.

Of course, it is limited to research, and it may achieve a breakthrough. As for solving the Riemann hypothesis, there is no need to think about it.

Xiao Yi recalled the paper on the Riemann hypothesis that he had read before.

The origin of the Riemann hypothesis comes from Riemann’s observation that the frequency of prime numbers is closely related to the properties of a carefully constructed so-called Riemann zeta function ζ(s).

He then made an assertion: All non-trivial zeros of the Riemann zeta function are located on the line Re(s)=1/2.

The reason why this conjecture is so important is that first of all, it involves the distribution law of prime numbers, which is something that countless mathematicians dream of.

Secondly, it is because there are many propositions in the mathematical world that can only be established on the premise that the Riemann hypothesis is proved, and at the same time, there are many propositions that can only be established after the Riemann hypothesis is falsified.

There are thousands of these propositions, and they are not just mathematical propositions, but also some physical inferences.

Therefore, the result of the Riemann hypothesis is very important. Whether it is proved or falsified, it can make a considerable part of the propositions become theorems, and these theorems will also provide great help in solving other problems in mathematics.

But obviously, as such an important hypothesis, its difficulty in proving is self-evident. Since it was proposed by Riemann in 1859, it has been almost 200 years, attracting almost every generation of the best mathematicians in the mathematics world to try, but it has never been solved.

"The best results of the current Riemann hypothesis seem to be concentrated on the Conray critical line, right?"

Thinking of this, he simply checked the relevant information.

Soon he found the content, "Oh! It turned out to be the critical line theorem that Selberg first came up with."

In 1942, Selberg proved that for the critical line of the Riemann zeta function, the proportion of zeros on it in all non-trivial zeros is greater than zero.

This is a very important breakthrough in the Riemann hypothesis, also known as the critical line theorem. After that, the mathematical community officially began to study the approximation of critical lines.

For example, Selberg's proof, through the calculation method mentioned in his paper, can get a result: about 5% to 10% of non-trivial zeros fall on the 1/2 critical line.

So after that, Selberg's method began to be vigorously developed in the mathematical community.

Levins raised this result to 34%, and then raised this number to 34.74% in the year he died of a brain tumor. Although this improvement is very small, it is also admirable to his spirit, which can be called: If you hear the truth in the morning, you can die in the evening.

After that, it was Conroy who approached the critical line to 40%.

After Kang Rui’s 31 years, there was no breakthrough until 2020, which was last year. Four mathematicians, Pratt, Robles, Zaharescu and Zeindler, raised the result to 5/12, or about 41.7%.

It was almost a very small improvement - but it is undeniable that this is the strongest result of the Riemann hypothesis so far.

If this critical line can be pushed to 100%, it is equivalent to proving the Riemann hypothesis. Therefore, many mathematicians in the entire mathematics community are working in this direction.

Xiao Yi quickly found Kang Rui’s paper and the paper published by the four mathematicians last year. This paper was published in "Res Math Sci", but it is only a third-zone journal. The method used in it is probably just a simple optimization of the method in Kang Rui’s paper, so it was not accepted by a better journal.

Of course, he did not dislike it, but read both papers carefully from beginning to end. Until the end, after understanding the method, he was stunned.

"Oh my god? Tao is right. This new expansion can really be used in the study of Riemann hypothesis?"

After just reading the two papers, he could easily find that the Xiao polynomial expansion method can be combined with Kang Rui's method and the critical line can be approached again.

How much closer it can be, he still needs to calculate carefully.

Thinking of this, he immediately started to work.

It just so happens that his paper is still missing an example of application. For a paper like his that mainly proposes a new method, finding an application case to illustrate the role of this new method is indispensable in the paper, so that he can introduce the use of his method to the mathematical community.

Hmm... Using the Riemann hypothesis to demonstrate it should be enough to show how awesome this method is, right?

In this way, he spent a whole day calculating, and finally successfully approached the critical line to 50%.

"Done!"

Putting down the pen in his hand, he clapped his hands.

"50%, not bad, it should be able to be improved a little bit, but forget it, it's so late."

And he could see that even if he continued to calculate, it would be impossible to really prove the Riemann hypothesis.

It was still a long way off.

And he felt that trying to crack the Riemann hypothesis from the perspective of critical line approximation was not the right way, but like walking on a narrow path, never knowing what difficulties would be encountered at the next corner, and maybe it would be completely blocked.

If you want to prove the Riemann hypothesis, you should try from other angles.

"That's it, organize the paper, and then post it on arxiv first."

"Well, according to the role of this new polynomial expansion method, the four major journals should accept it."

Xiao Yi knew very well how great the potential of his [Xiao's Polynomial Expansion] method was, and the breakthrough in the critical line theorem of the Riemann hypothesis was just a small role.

Of course, he didn't have the energy to fully tap the potential of this method, and who knows how many papers he could write.

Let's leave it to the mathematics community.

In this way, after spending some time to organize the entire paper, he uploaded it to arxiv.

It was already late, so he simply tidied up his desk, then washed up and went to bed.

…

Publishing papers on arxiv requires review, of course there are always exceptions, such as those real experts.

If experts publish papers on arxiv, they only need to go through a simple system check for plagiarism, and then they can pass the review and be directly visible to everyone.

And Xiao Yi is now more or less such an expert.

So after he fell asleep, his paper appeared on arxiv soon.

…

The United States adopts a multi-time zone system, which means that the time is different depending on the time zone.

Therefore, when Xiao Yi's Los Angeles entered 0 o'clock in the evening, it was already nine o'clock in the morning in Germany.

"A new polynomial expansion approaches the critical line theorem of the Riemann hypothesis to 50%?!"

Bonn, Max Planck Institute for Mathematics.

Faltings, who had just arrived at his office, was going to check arxiv to see if there were any new papers yesterday as usual, when he saw this new paper.

"A new polynomial expansion? Can it push the critical line to 50%? What a joke."

Faltings felt a little bit unconvinced.

Last year, the critical line finally got a little bit of progress, and this year, even a few months have not passed, someone can take such a big step forward?

Are you kidding!

However, when he moved his eyes to the author's column, he was stunned.

Xiao Yi? !

Chapter 116 Riemann hypothesis is not worth mentioning?

Seeing this name, Faltings silently moved the cursor on the screen to the pdf link next to the title and clicked it.

Entered the pdf interface of the paper, downloaded it, and then opened the pdf file viewer to read it.

"It turned out to be Xiao Yi's paper... Isn't he in UCLA now? How can he still have the energy to publish a paper?"

Faltings couldn't help but think like this.

And the result is such an important one.