The top student must be diligent

"Abstract...Based on the automorphic theory inversion of Etale algebraic varieties based on the classification sieve method, the basic group information is extracted from the L-function...After analytical continuation processing, a polynomial in a Fourier-like expansion form is performed Expand... This article mainly demonstrates the effect of using it to approximate the critical line of the Riemann Hypothesis, and finally succeeded in approaching the critical line theorem to 50%, but I believe there is still room for improvement. "

The critical line theorem of the Riemann Hypothesis, which has not been broken for a long time, has been directly improved to 50%!

Faltings can guarantee that this result can be said to have a chicken-blood-like effect on the entire mathematical community, even if it does not really prove the Riemann Hypothesis.

Because it means that after more than thirty years, the critical line approximation method is still a method that can be tried to solve the Riemann Hypothesis.

It can reignite further discussion of critical line approximation methods in the mathematical community and allow more people to try it.

This is the Riemann Hypothesis!

Even the slightest possibility will arouse the enthusiasm of the entire mathematical community.

As for last year’s paper, it’s not important, because the improvement from 40% to 41.7% is not really a huge achievement. Faltings has also read that paper, and the methods used in it are not that eye-catching. , even...he can know what the method is just by reading the summary.

He once came up with this result out of boredom, but he didn't like it, so he put it aside long ago.

Only the breakthrough results in Xiao Yi's paper can truly prove that as long as they continue to develop new mathematical tools, they can help them achieve further results in the proximity line approximation method.

However, when Faltings read this summary, he didn't know why, but he saw something in it...

Versailles feeling.

Such a breakthrough in the Riemann Hypothesis, but Xiao Yi only presented it as a case?

Do you think his polynomial expansion is more powerful?

If this is not Versailles, Faltings doesn’t know what Versailles is.

"I want to see how important your new polynomial expansion is. Even the Riemann Hypothesis is ignored."

Faltings couldn't help but become curious, turned the page down, and entered the main text.

This paper is not long, only 21 pages. Excluding the space occupied by literature references, there are only 20 pages of text content.

At the same time, the first 8 pages are used to introduce the new polynomial expansion, and the remaining 12 pages are all about approximating the critical line of the Riemann Hypothesis. Of course, this aspect does not require much content. Kang Rui’s This paper is only 26 pages long.

However, Faltings knew very well that the content of the first eight pages was the core content of this paper.

"Well, it's very short. You can almost finish it in about half an hour."

Faltings thought so at first, but as he started to read it, he realized that these 8 pages might contain more technical content and be more complicated than the 20 pages of other papers.

He also read it far more carefully and cautiously than any other paper, for fear of missing any small point in it.

Until two hours later.

Faltings finally finished reading the 8 pages.

The desk was already piled with scratch paper, all used to verify the content of these eight pages, and his face was already full of disbelief.

"This polynomial expansion... is actually real..."

How to describe this new polynomial expansion?

Faltings can only say that in the field of complex analysis, its role is no less important than Taylor expansion, Fourier expansion, etc.

Whether it is Taylor expansion, Fourier expansion, etc., their status in the mathematical world is unquestionable. For example, Taylor expansion, as the most basic method in calculus, exists in almost the entire mathematical world. No mathematician would say that he did not understand Taylor expansion, and he would be laughed at.

Now, Faltings has seen this new development, with such potential.

At least in the domain of complex numbers, this is obvious.

"It can more fully display the information hidden in some original algebraic expressions in the complex number field, which can be used to help analyze almost all problems in mathematics!"

Finally, Faltings understood why in this paper, the Riemann Hypothesis could only be used as a case demonstration.

Indeed, compared to this new polynomial expansion method, the Riemann Hypothesis is nothing at all. It is just a 50% critical line. In the face of such heavyweight results, it is not worth mentioning at all.

Unless it's Riemann's theorem.

Faltings couldn't hold back and returned to page 1, intending to read these 8 pages from beginning to end.

As for what the next 12 pages were, he couldn't care less, because after reading these 8 pages, he already knew what the next 12 pages were about.

In this way, Faltings spent nearly an hour reading these 8 pages again.

Finally, he leaned back strategically and leaned on the back of the office chair.

"That kid... did something so incredible again, it's really..."

"Does he have any limits in mathematics?"

He smiled helplessly, and then he began to think.

Using this new expansion...well, let's call it Xiao's expansion.

Using Xiao's expansion seems to be helpful for his recent research.

As a top mathematician, the problems he studies are basically the most cutting-edge problems in mathematics, and the Riemann hypothesis is among them.

Of course, he and Xiao Yi have the same idea that critical line approximation is not the right way, so he has been thinking about the possibility of using other methods to solve the Riemann hypothesis.

Xiao's expansion seems to help him think about the possibility in this regard.

By the way, there is also the Landau-Siegel zero point conjecture.

Faltings remembered that Zhang Yitang was studying this problem.

In this way, Zhang Yitang is lucky. With Xiao Yi's new method, it seems that solving the Landau-Siegel zero point conjecture will become much easier, especially when they are about to cooperate...

Faltings estimated that it would not be long before the Landau-Siegel zero point conjecture was solved.

"Is this the benefit of having a genius collaborator?"

Suddenly, there was a knock on the office door.

Schultz walked in.

He walked to Faltings with two cups of coffee in his hand, put one of them on the latter's desk, took a sip, and asked: "I was wondering why I didn't see you today. It turns out that you stayed in the office all morning. What were you doing?"

"Reading a paper."

"Oh?" Schultz raised his eyebrows, glanced at the computer screen, and said: "It must be very long."

"Not long, only 21...well, it should be 8 pages."

"8 pages? So few, you can actually read it for a whole morning?" Schultz was a little surprised.

Faltings stared at Schultz and took another sip of coffee, then said: "Xiao Yi wrote it."

"Walter cough cough..."

Hearing the name, Schultz's eyes widened, and then he was choked by the coffee he just drank.

Seeing this scene, Faltings laughed and fell backwards, and the prank was successful!

Let this kid threaten me with the things that happened when he was in Princeton?

He should let him know what it means to respect the elderly and love the young!

However, although he was teased, Schultz didn't have time to care about it. When his throat was almost comfortable, he immediately asked: "When did Xiao Yi write the paper."

"Well... let me see."

Faltings said while glancing at the publication time of the paper, and then replied: "It was at nine o'clock this morning. I just opened arxiv today and it popped up."

"You didn't even tell me when you saw it!"

Schultz complained, and then immediately leaned over and looked at the paper.

The title of the paper also immediately surprised him.

"He actually started to study the Riemann hypothesis now?"

"And... how long has it been since the Princeton conference! Isn't he with Terence Tao now? How did he push the critical limit theorem of the Riemann hypothesis so far?! Aren't they studying the x^2+1 prime number problem?"

After he finished reading the abstract, he narrowed his eyes.

"Wait, this abstract... why does it give people the feeling that he doesn't attach much importance to this breakthrough in the Riemann hypothesis?"

"Is his polynomial expansion the most important?"

"You can see that too." Faltings stood up with a smile, picked up his cup of coffee, drank it in one gulp, and then said: "You can read it slowly, I'm going to have lunch first."

Faltings left, and only Schultz was left in the office.

He sat in front of the computer and began to read the paper seriously like Faltings just now.

When Faltings came back, he saw Schultz scratching his enviable long hair, muttering: "This expansion... This expansion... My God, how did he come up with it?"

"How is it?"

Faltings smiled.

Schultz came back to his senses, turned to look at Falkins, and immediately pointed at the paper on the computer screen and exclaimed: "This polynomial expansion is really incredible! Although I have studied his Etale algebraic cluster automorphism theory many times, as well as his classification sieve, I never thought that it could be used in this way!"

"He actually has such a deep study of complex analysis!"

"Yes." Falkins nodded slightly.

"He always brings great surprises to the mathematical world, doesn't he?"

"I think, if the Riemann hypothesis is really proved in the future, this new polynomial expansion will definitely play an extremely important role in it."

Hearing Falkins's evaluation, Schultz did not refute.

There is no need to refute.