The top student must be diligent.

Chapter 285 Manuel's Shock and Relief

Princeton University, Department of Mathematics.

"Professor, I have a problem now... You see, I am trying to use the method of analytical continuation to solve the problem of this function, hoping to obtain more information through analytical continuation."

"I have read many related papers, and they generally do this in this step."

"But now that I've done that, I haven't achieved the same results as in other papers, and I haven't gotten the information I want."

In Manuel Bhargava's office, he listened to Sanjay's questions.

"Hmm... So what you are trying to study now is the properties of the gamma function?"

Manuel asked as he flipped through the draft paper Sanjay handed him.

"Yes."

Sanjay nodded. “I mainly want to understand the behavior of this gamma function on the entire complex plane, especially its behavior near some special points.”

Manuel nodded.

Using the analytical continuation method to study the gamma function is indeed a very normal approach, and most people will try to use this method to study the gamma function.

but……

Why did Sanjay have difficulty with this?
He looked at it carefully and began to analytically extend the gamma function in his mind using common methods.

First, define it on the right half plane Re(z)>0: [Γ(z)=∫^∞ t^(z-1) e^(-t) dt]

We then exploit the property of the gamma function Γ(z+1)=zΓ(z), allowing its definition to be extended to the entire complex plane.

Next…

Soon, his eyebrows raised, and then he smiled and said to Sanjay: "Oh! I think I know what problem you are facing."

"The gamma function you found has some special properties, or in other words, some unexpected properties, and these unexpected properties obscure the information you want to obtain."

"Therefore, if you want to obtain this information by analyzing the extension, my suggestion is that you can try to analyze the function after the extension more deeply and use other techniques to help you find some key information."

"Yes, it is like that."

After listening to the instructor’s explanation, Sanjay was stunned.

"Unexpected nature?"

“Do I need to use some other techniques?”

For a moment, he fell into thought.

Seeing him thinking, Manuel gave him a hint: "In fact, you can take a look at Xiao Yi's paper on the analysis of elliptic recurves, and then use this method, and your problem will most likely be solved. The analysis of elliptic recurves can specifically solve the problem you are facing."

Sanjay's eyes lit up immediately. "Xiao Yi's paper? Great! I'll go and read it later!"

Looking at Sanjay's expression, which seemed full of trust in his idol, Manuel shook his head with a smile.

Although these students of his were his students, each of them admired Xiao Yi even more.

But he didn't say anything. Anyway, this kind of thing is too normal nowadays.

Just like last century, many mathematicians admired Grothendieck, and now, people just have a different object of worship.

Even he himself was once one of those who admired Grothendieck, but now, as he is getting older, it is no longer a question of admiration or not, not to mention that Xiao Yi is younger than him.

But this did not prevent him from having admiration for Xiao Yi.

Mathematics is a field that truly relies on strength. It is absolutely not a field where any cheater can survive. As long as you have the strength, you will be respected by the entire mathematics community.

Xiao Yi has already won the admiration of the entire mathematics community.

……

Soon, Sanjay returned to their laboratory and came to his workstation.

Sitting next to him was Chen Muhua, and he immediately said to Chen Muhua: "Hey, I just asked the professor about my problem, and he quickly found the problem and recommended that I learn the analysis of elliptic recurves taught by your predecessor professor!"

Chen Muhua smiled and said, "That's a good suggestion indeed! Elliptical recurve analysis should be very helpful for problems like the one you're facing."

"Well! Finally, it gives me a reason to study Xiao Yi's thesis." Sanjay said.

Then he opened the browser and started searching.

"Hmm...it seems that all of Xiao's papers are published on his personal website. Chen, please input Xiao's personal website for me so that I don't have to look for it."

Chen Muhua shrugged and said, "I thought that as his loyal fan, you should be very familiar with his website."

Then he came to Sanjay and helped him enter the address.

Sanjay said, "Oh! Even a devout Hindu needs to ask someone for directions to Varanasi."

Chen Muhua rolled his eyes and said nothing more. He quickly entered Xiao Yi's personal website address on Sanjay's website and pressed Enter.

"All right."

Then he stood up and returned to his seat.

Sanjay then started looking for it. Although the website was in Chinese, the browser's built-in translation could still be used.

But soon, he frowned and asked, "Huh? Why didn't I find the analysis of the elliptic recurve?"

Chen Muhua was puzzled: "Isn't it just on the paper page?"

“I used the search function, but it didn’t come up,” Sanjay said, pointing at his computer screen.

Chen Muhua suddenly felt even more puzzled.

Xiao Yi’s personal website also comes with a very simple search function. However, although it is very simple, since the number of papers is not large, the search should be able to find them quickly.

There is absolutely no doubt about Professor Xiao's coding ability.

"Then, just look for it on the homepage."

Although he was confused, he then spoke.

If you can’t find it, just go find it.

So he went back to the homepage and started looking for it for Sanjay.

But after searching for a while, his eyes widened.

He looked in shock at a column on the homepage, which directly labeled the Riemann hypothesis.

It was obviously not there when he saw it before!
"Wait, look at this. If I'm not mistaken, this thing is... the Riemann hypothesis? Take a look, isn't it?"

Sanjay was stunned for a moment, then took a look and also showed a surprised expression: "Yes... yes!"

He immediately guessed: "Could it be that Professor Xiao has also begun to announce his research progress?"

However, Chen Muhua didn't think so and said, "Click in and take a look first!"

Sanjay nodded immediately and clicked on the link.

When I went in and took a look, the overall background was basically the same as Xiao Yi's personal website, and in the middle, there were five underlined links.

These are the names of five papers. Clicking on them will take you to the PDF files of these five papers.

The first paper was the one on the analysis of elliptic inflection that Sanjay was looking for.

And the second one...

That's what they can't understand.

Discussion on High Dimensional Modular Curves

There is also a third... a fourth... and a fifth.

Proof of Artin's conjecture

CM Elliptic Curves and Hecke Characteristic

Proof of the Riemann Hypothesis

"Gift Crab Special!"

After reading it, the two of them jumped up at the same time, holding their heads and exclaiming. Their actions naturally attracted the attention of other people in the laboratory.

"Hey, what's up with you two?"

Their shocked expressions soon made others wonder, and they asked questions one after another.

"Oh! You won't believe what we saw."

Sanjay said with an exaggerated look on his face.

"what exactly is it?"

The others became even more curious.

At this time, a fellow disciple next to them walked over, took a look, and then immediately jumped up in shock, even higher than them. "Fuck it!"

Seeing the reaction of the third person, the other fellow disciples became even more curious.

"Hey, hey, hey, you guys, have you guys colluded with each other to cheat us?" others said.

Then someone called the fourth person next to them: "Jack, go and see what they are so shocked about!"

Jack stood up helplessly and walked over while complaining, "Hey, how boring! We are all graduate students in the Department of Mathematics at Princeton University, so we don't need to play these childish games... Wang Defa?!"

When he walked in front of the computer screen, he was also shocked.

"Hey, hey, hey, hey! You four, are you guys in collusion?"

The others immediately spoke unhappily.

At this time, the others finally couldn't help themselves and walked over to see with their own eyes what was going on.

Of course, there is also one person who is so convinced that they are simply lying that they can't help but watch.

But after almost everyone looked over and was shocked, this person finally hesitated a little, but he still didn't move, and kept saying: "Please, can you guys not be so tacit?"

However, at this time, the group of Princeton University mathematics graduate students gathered in front of Sanjay's computer had already started a discussion.

"Is this true? Did he actually prove it?"

"Since he sent it...it must be true, right? After all, he is the smartest person who has ever lived!"

"I can't believe it, I really can't believe it... I haven't heard from him for such a long time. It turns out that he has actually solved this problem?"

"Oh my god, it's only been a short time! Is he still a human? Why do I feel like he's already reproductively isolated from ordinary humans?"

"But the problem is... this is the Riemann hypothesis! Did he really prove it?"

……

After hearing this, the person who was still sitting in his seat finally understood what this group of people were shocked about.

Xiao Yi, did you really prove the Riemann hypothesis?

He immediately shouted, "Please don't lie to me! I really want to come over and take a look now!"

But the group ignored him.

He stood up and started walking over. It seemed as if the scenes that might happen next had already appeared in his mind, just like the plots in those videos, where a group of people were shocked by something, which caught the attention of the last person. As a result, when that person walked over and took a look, he realized that he had been fooled.

So, until finally, he walked over and took a look, and then, he was also shocked.

It turned out to be true!
"Hou Li Xie Te! Why didn't you tell me earlier! This is actually true!"

But they ignored his excitement. After all, they were all shocked by this incident and had no time to care about other people's shock.

Perhaps their voices were finally heard by Manuel in the next office, so he walked over, and when he saw a group of people gathered together, he frowned and said, "Hey, what are you doing? Noise is not allowed in my lab!"

Then, he received shocking news.

"Professor, Professor Xiao Yi...proved the Riemann hypothesis!"

His students all looked up at their respected mentor and told him the news.

These students all know very well that their teacher is one of the initiators of the Prime Number Pioneer Project. After all, it was this teacher who initially attracted the attention of other professors when he and another professor, Professor Okunkov, were studying Xiao Yi's elliptic recurve analysis. Finally, after discussion, they decided on this cooperation plan.

The result is now...

They were suddenly defeated by that one person...

Manuel was in disbelief at the first news.

How can it be!

That's the Riemann hypothesis!
How long has it been since?

No one in the world can solve the Riemann hypothesis so quickly!

But then, he suddenly realized that the other person was Xiao Yi.

Xiao Yi...

I stood there for a long time, with the name lingering in my mind for a long time.

In the end, he didn't say anything, but just walked over. He wanted to know where these students of his got the news.

Soon, he came behind them and saw the page displayed on the computer screen.

Then he fell silent again.

He had the same reaction as several previous students.

This is actually true...

His students also remained silent, just looking at their professor.

They all wanted to know how their professor would react to this matter.

Until finally, they saw a kind of relief on the professor's face, as if he was saying: Yes, the other party is Xiao Yi!
His mood became calm, and then he asked: "Where did you see this website?"

Sanjay said, "It's on Professor Xiao Yi's personal website. You know, you just recommended me to take a look at his analytical method for elliptic inverse curves. Then I went to this website and looked it up, and I found this."

"Oh, I see." Manuel nodded, then turned and left without saying a word.

As the professor left, everyone in the laboratory immediately started talking.

Of course, their voices were a little quieter.

"So, it seems that all the big guys in the Prime Number Pioneer Project have lost to Xiao Yi?"

"Come on, this is not shameful, that's Xiao Yi!"

"That's the real GOD!"

"I bought GOD."

At this time, someone suggested: "Why don't we open the paper and take a look first!"

This proposal was quickly agreed upon, so Sanjay operated the computer and, at the suggestion of everyone, directly opened the last paper, "Proof of the Riemann Hypothesis."

As a result, after clicking on it and looking for a while, they fell silent.

Even for these mathematics graduate students at Princeton University, they still found it a bit difficult to read this paper.

For a moment, they looked at each other.

"How about... let's forget it?"

"Forget it."

They all laughed and dispersed, returning to their seats. It was still too difficult for them to understand this kind of paper.

However, this did not stop them from starting to spread the news online.

Riemann hypothesis has been solved by Xiao Yi!

……

In Manuel's office, he first made a cup of coffee, then slowly sat down in front of his computer and entered Xiao Yi's personal website.

Then, he quickly found the website.

Looking at the domain name of this website, he sighed helplessly.

This domain name is completely compatible with the content.

He then turned his attention to five papers.

After taking a quick look at their titles, he soon found that "Discussion on High-Dimensional Modular Curves" and "Proof of Artin's Conjecture" attracted all his attention.

"High-dimensional modular curves? So his most important method is to develop the high-dimensional case of modular curves?"

"And then there is this... Artin guessed..."

He sighed, "He actually chose the path that Artin had guessed."

However, this approach was almost immediately abandoned in their Prime Number Pioneer Project.

"Okay, let's start watching."

Of course, before that, he did not forget to share this website with the discussion group of their Prime Number Pioneer Project, and attached a message: [Xiao Yi has completed the proof of the Riemann hypothesis. ]

Then, he ignored the question marks that kept replying and started reading the paper.

……

(End of this chapter)