The top student must be diligent.

Chapter 115 "A new polynomial expansion approaches the critical line theorem of the Riemann hypothesis to 50%"

"If our final agreement can really be selected by the World Bank, Xiao Yi will definitely be the first to receive the credit!"

"I think so too." Tao Terence nodded in agreement.

Maynard, of course, agreed.

Before working with Xiao Yi, Xiao Yi was seen by them as a super smart genius with talents that amazed the world.

And now after working together, Xiao Yi has become a god-level teammate for them.

Now they are all led by this god-level teammate.

"Well..." Kleinlock said, "So, when the $1000 million reward is distributed, I think Xiao Yi should get at least $500 million of it."

Tao said, "Hey, I don't think 600 million is a big problem."

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 begun discussing how to divide the 1000 million US dollars.

Of course, this is also because after the two most critical problems have been solved, they have become very confident in obtaining the 1000 million US dollars.

Is there any other group that can come up with a protocol that can not only prevent the trading platform from stealing, but also avoid hacker intrusion like theirs?

Hearing the conversation between the three professors, Xiao Yi didn't know whether to laugh or cry, and quickly waved his hands and said, "No, no, there are other parts of the entire protocol that have not been completed. I can't complete them all by myself, not to mention that I need to write them into programs."

"..."

After some discussion, they finally made a decision. Xiao Yi would take 600 million US dollars, and the remaining 400 million would be distributed among Tao and others according to their respective contributions.

Things like programming were done by Terence Tao and Kleinlock, and some other work in mathematics was done by James Maynard.

As for Xiao Yi, he doesn't have to do anything from now on.

After solving these two most troublesome problems, if he also takes care of other things, wouldn't others be even more embarrassed when the time comes to divide the money?

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

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

He naturally has things of his own to do.

The first thing was to organize his paper "Xiao's Polynomial Expansion".

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

As for whether they need to worry about their competitors learning from them, there is no need to worry.

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

To be more conservative, even if they really understood this paper, it is still a question whether they can immediately think of how to use it to defend against classification screening attacks, not to mention the technical difficulties involved.

Perhaps in this world, only Xiao Yi could think of a way to solve the problem of classification and screening based on it.

……

"Hmm... I heard from Terence Tao that this thing can also be used to study the Riemann hypothesis?"

While organizing his thesis, Xiao Yi thought about it in his mind.

Of course, it is limited to research, and maybe some breakthroughs can be achieved. As for solving the Riemann hypothesis, there is definitely no way around it.

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

The origin of the Riemann hypothesis comes from Riemann's own 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 asserted that all non-trivial zeros of the Riemann zeta function are located on the straight 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 mathematics that can only be established based on the premise that the Riemann hypothesis is proved. At the same time, there are also 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 number of propositions become theorems, and these theorems will also provide great help in solving other problems in mathematics.

But obviously, as such an important conjecture, the difficulty of proving it is self-evident. It has been almost 1859 years since it was proposed by Riemann in 200. It has attracted almost every generation of the best mathematicians in the mathematics world to try, but it has never been solved.
"The best results in the current Riemann hypothesis seem to be concentrated on the Conrui critical line, right?"

Thinking of this, he simply looked up some relevant information.

He quickly looked up the content, "Oh! It turns out to be the critical line theorem first proposed by Selberg."

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

This was 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 critical line approximation.

For example, Selberg's proof, by calculating the method mentioned in his paper, can get a result: about 5% to 10% of the 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 improved this result to 34%, and then to 34.74% in the year he died of a brain tumor. Although this improvement is very small, one cannot help but admire his spirit. It can be said: If I hear the truth in the morning, I can die in the evening.

After that, it was Kangrui who pushed the critical line to 40%.

There was no breakthrough in the 31 years after Kangrui until 2020, last year, when four mathematicians, Pratt, Robles, Zaharescu and Zeindler, raised the result to 5/12, or about 41.7%.

It is almost a tiny 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 would be equivalent to proving the Riemann hypothesis. Therefore, in the entire mathematical community, many mathematicians are working towards 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 zone 3 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 despise them, but read both papers carefully from beginning to end. Until the end, when he understood the methods, he was stunned.

"Oh my god? Terence Tao really got it right. Can this new development really be used in the study of the Riemann hypothesis?"

After just reading the two papers, he was able to easily find that Xiao's polynomial expansion method could be combined with Kangrui's method to bring the critical line closer again.

How close it can be still requires careful calculation.

Thinking of this, he immediately started to take action.

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

Well... 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, he successfully brought the critical line to 50%.

"Finish!"

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

"50%, not bad, it should be able to go up a bit, but forget it, it's getting late now."

Moreover, he could see that even if he continued calculating, it would be impossible to truly prove the Riemann hypothesis.

There is still a long way to go.

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

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

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

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

Xiao Yi is well aware of the great potential of his [Xiao's Polynomial Expansion] method, and the breakthrough in the critical line theorem of the Riemann hypothesis is only a small part of it.

Of course, he doesn't have the energy to fully explore the potential of this method, otherwise who knows how many papers he could have written.

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, washed up and went to bed.

……

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

When big names publish papers on arxiv, they only need to go through a simple plagiarism check by the system, and then they will pass the review and be directly visible to everyone.

And Xiao Yi can now be considered as such a big shot to some extent.

So when he fell asleep, not long after, his paper appeared on arxiv.

……

The United States uses a multiple time zone system, which means that the time is different depending on the time zone.

Therefore, when it was midnight in Los Angeles where Xiao Yi was, 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%?!"

Max Planck Institute for Mathematics in Bonn.

Faltings had just arrived at his office. As per his daily habit, he planned to go to arxiv to see if there were any new papers published yesterday. As a result, he saw this new paper on it.

"A new polynomial expansion? Pushing the critical line to 50%? You must be kidding."

Faltings felt a little unconvinced.

Last year, this critical line finally got a tiny push forward, and this year, even within a few months, someone was able to take such a big step forward?
Just kidding!
However, when he moved his eyes to the author's column, he was stunned.

Xiao Yi? !
(End of this chapter)