"Elliott-Haberstam Conjecture!"
Hearing Faltings's words, Xiao Yi was immediately stunned.
Elliott-Halberstam conjecture is also a conjecture about prime numbers in number theory.
And it is of great significance to the mathematical community - it can help mathematicians save more effort when studying the distribution of prime numbers.
As for the distribution of prime numbers, it refers directly to the most profound and influential issue in mathematics - Riemann Hypothesis.
Therefore, proving the Elliott-Halberstam conjecture is very important to the mathematical community.
In the words of Terence Tao, proving this conjecture is a dream.
But obviously, dreams are hard to come by.
The purpose of the Elliott-Halberstam conjecture is to prove that the θ value of the distribution level of prime numbers is less than 1. In the 1960s, Bombieri and another mathematician proved that the θ value is less than one-half, which is still one-half gap from [1]. However, this one-half gap seems to have become a gap, which has deeply stumped the mathematical community and has never been able to achieve a breakthrough.
However, in modern times, this gap has gradually changed. For example, Zhang Yitang broke it to the level of 0.5017, thus completing the first great progress on Twin Prime Conjecture in one fell swoop.
Back to Twin Prime Conjecture, the reason why Faltings mentioned this conjecture to Xiao Yi is because, once this conjecture is proved, it can directly reduce the gap between Twin Prime Conjecture to 6.
To a certain extent, reaching this result is equivalent to proving another conjecture, called [Sexy Prime Conjecture]. A pair of prime numbers with a difference of 2 is called a twin prime, and a pair of prime numbers with a difference of 6 is called a sexy prime. Whether there are infinite pairs of prime numbers with a difference of 6 is called Sexy Prime Conjecture.
Although I don't know why such a pair of prime numbers is called sexy, maybe this is the aesthetic taste of mathematicians.
"Yes, it's the Elliott-Halberstam Conjecture. Don't you think your idea is particularly suitable for studying this problem?"
"Of course, I'm not asking you to prove this conjecture. I'm just asking you to think about whether it can help you with your current problem from the perspective of this conjecture."
"Far Abelian Geometry, plus Automorphic Forms, I believe these two things can play an unexpected role when combined."
"What do you think?"
Faltings said with a smile, then picked up the cup next to him, took a sip of water, and left time for Xiao Yi.
At this moment, Xiao Yi has also begun to think.
This suggestion from Faltings caused a sudden burst of inspiration in his mind.
This also made him marvel. The experience of the old mathematician was indeed quite powerful.
Although people praise his mathematical thinking for being very independent and not affected by empiricism, at certain times, the role that experience can play is still quite huge.
With the burst of inspiration, he started writing on the blackboard next to him after a moment.
[∑nxθ(n)λ(nhi)2=∑d1|P∑d2|Pμ...]
[θ(n)= Q2([d1, d2])φ([d1, d2])...]
After a while, the blackboard, which had very little blank space, was almost used up by Xiao Yi.
However, at this moment, Faltings picked up the blackboard brush and helped him erase the previous handwriting.
At this time, Faltings was once again shocked by Xiao Yi's quick thinking.
He had no idea that the thought he had just spoken would immediately come into the young man's mind.
Is it because of the young man's quick reaction or because of his extraordinary talent?
In the end, he could only sigh in his heart that he was getting old, and then continued to help Xiao Yi clean the blackboard.
He didn't want to affect Xiao Yi's thinking because there was nowhere to write on the blackboard.
But at this moment, there was a knock on the office door, and Schultz walked in, followed by two people, Deligne and Bombieri.
"Professor, Professor Deligne and Professor Bombieri want to see you... eh?"
Seeing the scene in front of him, he was stunned.
Faltings is actually helping Xiao Yi clean the blackboard?
Good guy, is Xiao Yi so favored?
He has never been treated like this!
Deligne and Bombieri, who were following Schultz, were also surprised.
"Shh!"
When Faltings saw these three people coming in, he immediately raised his index finger in front of his mouth, asking them to be quiet and not to disturb Xiao Yi.
At this time, he also finished wiping the blackboard, leaving a whole blank space for Xiao Yi.
The three people who came in stopped talking and stepped forward to take a look.
And soon, as an expert in this field, Bombieri first saw what Xiao Yi wrote, and then Deligne and Schultz also quickly saw it.
Several people showed surprised expressions.
Bombieri: "He wants to study the Elliott-Halberstam conjecture from the perspective of Far Abelian Geometry?"
Deligne: "He actually understands Automorphic Forms?"
Schultz: "He actually did research on the Elliott-Halberstam conjecture?"
"Quiet, wait until he finishes writing." Faltings rolled his eyes and asked them to keep their voices down again.
Fortunately, Xiao Yi seemed to be completely immersed in the world of mathematics and didn't even notice anyone coming in.
The three Fields Medal winners finally calmed down and watched quietly. However, the more they watched, the more incredible they became.
Xiao Yi had unknowingly substituted Far Abelian Geometry into number theory's Automorphic Forms, and began to combine the two.
Automorphic Forms is an important concept in number theory, and applying Automorphic Forms to the study of prime number distribution is also a very important method in mathematics.
Mathematicians in China have previously won the second prize of State Natural Science Award in 2014 for their research in this area, which has also brought very important inspiration to the mathematics community.
And now, Xiao Yi has undoubtedly achieved an important breakthrough in this direction!
Perhaps, based on such a breakthrough, Automorphic Forms can play a more important role in the distribution of prime numbers and even more and more extensive issues!
Finally, when the blackboard was about to be finished again, the pen in Xiao Yi's hand stopped.
"Well... we can only stop here for the time being."
After taking another look at the entire process on the blackboard, Xiao Yi touched his chin and finally put down the blackboard pen in his hand.
Just when he was about to speak to Faltings, he heard applause from behind him.
"Incredible!"
"Awesome!"
"Perfect!"
Xiao Yi was stunned for a moment.
He turned around and saw three uninvited guests entering the room at some unknown time.
Four people gathered around him.
To elaborate further, four Fields Medal winners surrounded him, an underage boy.
"Uh, professors..."
But before he could say hello, Bombieri hurriedly asked, "What is your next idea?"