After listening to the papers recommended to him by Professor Bombieri that day, he later read the three papers by James·Maynard.
What I have to say is that Professor Bombieri's recommendation did bring huge help to Xiao Yi, so much so that he kept thinking about those three papers when he was on the plane.
Finally, he summarized a series of questions and ideas, and wanted to have a discussion with James·Maynard.
Of course, it is certainly impossible for him to fly directly to Oxford University where James·Maynard is located, so the most ideal method is naturally to communicate via email.
Soon, he took out the laptop he carried with him, entered his email address, and started sending emails to James·Maynard.
His thoughts and questions were edited on the plane, put into a PDF document, and then sent.
"Done."
I clap my hands, but I don't know when Professor Maynard will be able to reply.
"No matter, go to bed early. When I return to China today, I have to adjust my biological clock again."
Xiao Yi shook his head helplessly.
Thinking that in almost four months, he would have to fly to Princeton, and then he would have to adjust his biological clock.
Yes, when faced with Deligne's invitation that day, he naturally agreed in the end. After all, Faltings and Schultz were looking at him at the time.
He couldn't help but secretly make up his mind. After he became a super boss in the mathematics world in the future, he would do this kind of report or something. If it could be done in China, it would be done in China. It wouldn't be easy for anyone to do it!
Going abroad once a year is enough!
With such a dream in mind, he also started to rest after washing up.
The other side of the Eurasian continent.
United Kingdom, Oxford University, St John's College.
In an office, James·Maynard completed this morning's work.
Well, the main task today is to look at the papers written by his students.
What's great is that his students are also very good, and they have actually advanced the results he completed three months ago a little further.
In June, he published three papers, expanding the θ value of the prime number distribution level in the Bombieri-Vinogradov theorem to 0.6, which can be regarded as a huge breakthrough in their number theory community.
His students have now pushed this result to 0.617.
Although it is only 0.017, which does not seem big at all, this can be regarded as the characteristic of Analytic Number Theory.
Other mathematicians once jokingly called Analytic Number Theory scholars obsessed with such small progress.
However, for them, these small progress are of great significance. Just like in the 100-meter race, even if it is improved by 0.01 seconds, it is a world record breakthrough.
Simply put, with each advancement, technology becomes clearer and more unified.
"Well done, Richman. If you said before that you planned to use this paper as your doctoral thesis, I think it is completely enough."
Giving a thumbs up to the student who made this progress, Maynard said with a smile.
Then, the student named Richman suddenly became excited. Finally, his doctoral thesis was completed!
Seeing his student's happy expression, Maynard smiled slightly.
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.
"Huh? Any new mail?"
Maynard I thought about it for a while, and I didn't get off work for almost half an hour, so let's take a look at this email first.
He quickly entered the mailbox and took a look at this email.
"Hmm... called YiXiao? This name seems a bit familiar. Who is it?"
Maynard sat slightly leaning on the back of the chair, thinking about it in his mind, and soon thought of the name of the person he saw on the news some time ago.
"Huh? Could it be that genius from China? Why did he send me the email?"
Maynard is a little confused. What he does is Analytic Number Theory, and there is not much connection with Far Abelian Geometry that this genius is proficient in, right?
However, after he read the purpose of the visit stated in the email, his body that had just been leaning on the back of the chair immediately sat up straight, and his eyes immediately widened.
"Combining Far Abelian Geometry and Automorphic Forms? Starting from 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 specifically sent an email to discuss it with him.
He continued to look at the bottom of the email and saw Xiao Yi continuing to introduce it below.
[One problem that exists now is that we need to complete a key proof so that from the field of p-adic Hodge theory, Far Abelian Geometry can be completely algebraized, so that we can put it on Dirichlet L-function for discussion. To achieve the unification of the two, assuming that such a proof is successful, I can easily expand the distribution level θ value of prime numbers to more than 0.7 by simply trying it. And if the method used in your paper can be combined, this value can definitely be further expanded, and there is a complete chance of expanding it to 1.]
"Easily expand to more than 0.7? And there is a direct chance of expanding to 1?"
Expanding to 1, isn't it equivalent to directly proving the Elliott-Halberstam conjecture?
Maynard could no longer restrain his anxiety and directly downloaded the PDF document attached to Xiao Yi in this email.
He began to look.
Then, just looking at the front part shocked him.
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 improved the θ value to 0.65, which is 0.033 higher than the student named Richman he just praised!
"Didn't you say that this young man is studying Far Abelian Geometry? How come he knows so much about Analytic Number Theory?"
Maynard thought like this in his heart, but this did not affect him from continuing to look down.
The PDF document of Xiao Yi has 15 pages. The first five pages discuss the three papers of Maynard, and the next ten pages discuss the possibility of combining Far Abelian Geometry and Automorphic Forms.
His three papers originally mainly used Kuznetsov Trace Formula in the Automorphic Forms theory, so for him, even if he does not understand Far Abelian Geometry very well, he can roughly understand how important the combination of the two is.
In this way, time passed quickly, and even when it was time to get off work, he did not leave.
His students went to eat at the same time.
However, when these Oxford University graduate students returned here, they found their supervisor looking at the ceiling, thinking about something.
Richman, who was just praised today, boldly asked jokingly, "Professor, are you thinking about whether God exists now?"
Maynard finally came to his senses and said, "No, I was thinking about whether to go to China."