The top student must be diligent.

Chapter 76 Do you want to go to China?

After listening to the papers recommended to him by Professor Bombieri that day, he went back to read the three papers by James Maynard.

It must be said that Professor Bombieri's recommendation did bring great help to Xiao Yi, so much so that he kept thinking about the three papers while on the plane.

Eventually, he came up with a series of questions and ideas that he wanted to discuss with James Maynard.

Of course, he certainly couldn't fly directly to Oxford University where James Maynard was, so the ideal method was naturally to communicate via email.

Quickly, he pulled out his laptop, logged into his email inbox, and began sending emails to James Maynard.

His ideas and questions were edited while on the plane, all put into a PDF document, and then sent over.

"Finish."

Clap your hands, but I don’t know when Professor Maynard will be able to respond.

"No matter what, go to bed early. I'm going back home today and I have to adjust my biological clock again."

Xiao Yi shook his head helplessly.

Thinking that he would have to fly to Princeton in about four months, he would have to adjust his biological clock again.

Yes, when faced with Deligne's invitation that day, he naturally agreed in the end. After all, Faltings and Schultz were both looking at him at that time.

He couldn't help but secretly make up his mind that after he became a super boss in the mathematics world, he would give this kind of report in China if possible, because no one else could do it!
When it comes to traveling abroad, it’s enough to go once a year!

With this dream in mind, he began to rest after washing up.

……

The other side of the Eurasian continent.

St John's College, University of Oxford, UK.

In an office, James Maynard finished his work for the morning.

Well, the main work today was to look at the papers written by his students.

Fortunately, his students were also very good and actually took the results he had completed three months ago a little further.

In June, he published three papers, expanding the value of θ regarding the distribution level of prime numbers in the Bombieri-Vinogradov theorem to 0.6, which was considered a huge breakthrough in their number theory community.

His students have now pushed this result to 0.617.

Although it is only 0.017 and does not seem large at all, it is also a feature of analytic number theory.

Other mathematicians have joked that analytic number theorists are obsessed with such tiny advances.
However, for them, these tiny advances are of great significance, just like in a 100-meter race, even if the time is improved by 0.01 seconds, it will break the world record.

Simply put, with every step forward, the technology becomes clearer and more unified.

"Well done, Li Qiman. You said before that you planned to use this paper as your doctoral thesis. I think it is more than enough."

Maynard said with a smile, giving a thumbs-up to the student who made this progress.

Afterwards, the student named Li Qiman suddenly became excited. Finally, his doctoral thesis was completed!
Maynard smiled slightly at the joy of his students. However, at this moment, a pop-up window appeared in the lower right corner of his computer, reminding him that he had received a new email.

"Hmm? Any new email?"

Maynard thought about it and decided that since there was still about half an hour before he got off work, he might as well check the email first.

He quickly entered his mailbox and took a look at the email.

"Hmm... YiXiao? This name seems familiar. Who is it?"

Maynard leaned back in his chair, thought for a moment, and soon thought of the name he saw in the news some time ago.

"Hmm? Could it be that genius from China? Why did he email me?"

Maynard was a little confused. He was working on analytic number theory, so there shouldn't be much connection between it and the far Abelian geometry that this genius was proficient in, right?
However, after he read the purpose of the email, he immediately sat up straight, his eyes widened.

"Combining far-Abelian geometry with automorphic forms? Starting from the Kuznetsov trace formula and p-adic Hodge theory?"

Maynard thought about it for a moment and immediately realized that the other party must have read the three papers he published in June and then sent an email to discuss with him.

He continued to look at the email and saw Xiao Yi continuing his introduction.

[The problem now is that we need to complete a key proof to completely algebraize the far Abelian geometry in the field of p-adic Hodge theory, so that we can discuss it on the Dirichlet L function and achieve the unification of the two. Assuming that such a proof is successful, I just tried it and it was easy to expand the distribution level θ of prime numbers to more than 0.7. If you can combine the method used in your paper, this value will definitely be able to be further expanded, and there is a chance to expand it to 1. ]

"Easily expand to more than 0.7? And there is a direct chance to expand to 1?"

If it is expanded to 1, doesn’t it directly prove the Elliott-Halberstam conjecture?
Maynard could no longer suppress his anxiety and directly downloaded the PDF document attached by Xiao Yi in the email.

He began to look.

Then, just looking at the first part, he was shocked.

In the previous part, Xiao Yi mainly talked about the new method developed in his three papers, and made a simple supplement to this new method. Then, in just four pages, he raised the θ value to 0.65, which is 0.033 higher than the student named Li Qiman whom he had just praised!

"Isn't it said that this young man studies tele-Abelian geometry? How come he even knows so much about analytic number theory?"

Maynard thought so in his heart, but it did not stop him from continuing to read.

Xiao Yi's PDF document has 15 pages. The first five pages discuss Maynard's three papers, and the last ten pages discuss the possibility of combining far Abelian geometry and automorphic forms.

His three papers mainly used the Kuznetsov trace formula in the theory of automorphic forms. So for him, even if he did not understand far Abelian geometry very well, he could roughly understand how important the combination of the two was.

In this way, time passed quickly, and even when it was time to get off work, he did not leave.

His students eat on time.

However, when these Oxford University graduate students returned here, they found that their tutor was looking at the ceiling, thinking about something.

Lichtman, who had just been praised today, boldly asked jokingly: "Professor, are you thinking about whether God exists now?"

Maynard finally came back to his senses and said, "No, I'm thinking about whether I should go to China."

(End of this chapter)