The top student must be diligent.

Chapter 73: Surrounded by Four Fields Award Winners

"Elliott-Halberstam conjecture!"

When Xiao Yi heard what Faltings said, he was stunned.

The 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.

The distribution of prime numbers directly refers to the most profound and influential problem in academia - the Riemann hypothesis.

Therefore, proving the Elliott-Halberstam conjecture is of great importance to the mathematical community.
In the words of Terence Tao, proving this conjecture is a dream.

But obviously, dreams are hard to achieve.

The purpose of the Elliott-Halberstam conjecture is to prove that the distribution level of prime numbers, θ, is less than 1. In the 60s, Bombieri and another mathematician proved that this θ value is less than one-half, which is still one-half away from [1]. However, this one-half gap seems to have become a chasm that has deeply stumped the mathematical community and has never been able to make a breakthrough.

However, in modern times, this gap has gradually changed. For example, Zhang Yitang broke through it to 0.5017, thus completing the first major progress in the twin prime conjecture.

Back to the twin prime conjecture, the reason why Faltings mentioned this conjecture to Xiao Yi was that once this conjecture was proved, it would be able to directly narrow the gap of the twin prime conjecture to 6.

To a certain extent, reaching this result is equivalent to proving another conjecture called the sexy prime conjecture. A pair of prime numbers with a difference of 2 is called twin primes, and a pair of prime numbers with a difference of 6 is called sexy primes. Whether there are infinite pairs of prime numbers with a difference of 6 is called the sexy prime conjecture.

Although I don’t know why such prime number pairs are called sexy, perhaps 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 it from the perspective of this conjecture and see if it can help you with your current problem."

"Far Abelian geometry, combined with automorphic forms, I believe these two things combined can play an unexpected role."

"What do you think?"

Faltings said this with a smile, then picked up the cup beside him, took a sip of water, and left time for Xiao Yi.

At this moment, Xiao Yi has also started thinking.

Faltings' suggestion caused a sudden burst of inspiration in his mind.
This also made him exclaim in amazement, the old mathematician's experience was indeed quite impressive.

Although people praise his independent mathematical thinking that is not influenced by empiricism, experience can still play a huge role at certain times.

As inspiration struck, a moment later he began writing on the blackboard next to him.

[∑nxθ(n)λ(nhi)2=∑d1|P∑d2|Pμ……]

【θ(n)= Q2([d1，d2])φ([d1，d2])……】

After a while, the blackboard, which originally had little blank space left, 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 moment, Faltings was once again shocked by Xiao Yi's quick thinking.

He never expected that as soon as he expressed an idea, the young man would immediately have thoughts in his mind.

Is it because the young man himself reacts quickly, or is it because he is gifted?

In the end, he could only sigh in his heart that he was getting old, and then continued to help Xiao Yi wipe the blackboard.

He didn't want Xiao Yi's thinking to be affected by the fact that there was no place 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?"

He was stunned when he saw the scene in front of him.

Faltings, is he actually helping Xiao Yi clean the blackboard? My goodness, is Xiao Yi so favored?

He has never been treated like this!

Deligne and Bombieri, who were following behind Schulz, were also surprised.

"Shh!"

When Faltings saw the three people coming in, he immediately put his index finger in front of his mouth, asking them to be quiet and not disturb Xiao Yi.

At this time, he had also finished wiping the blackboard, leaving a whole blank space for Xiao Yi again.

The three people who came in stopped talking, walked forward and started to look.

Soon, as an expert in this field, Bombieri was the first to figure out what Xiao Yi wrote, followed by Deligne and Schultz.

Several people showed surprised expressions.

Bombieri: "He wanted to study the Elliott-Halberstam conjecture from the perspective of far-Abelian geometry?"

Deligne: "He actually knows how to defend himself?"

Schultz: "He actually also studied the Elliott-Halberstam conjecture?"

"Be quiet and wait for him to finish writing." Faltings rolled his eyes and asked them to keep their voices down again.

Fortunately, Xiao Yi seemed to have been completely immersed in the world of mathematics and did not notice anyone coming in at all.

The three Fields Medal winners finally calmed down and began to watch quietly, but the more they watched, the more incredible it became to them.

Xiao Yi had unknowingly substituted far Abelian geometry into the automorphic form of number theory and began to combine the two.
Automorphic form is an important concept in number theory, and applying automorphic form to the study of prime number distribution is also a very important method in mathematics.

A mathematician in China won the second prize of the National Natural Science Award in 2014 for his research in this area, which 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 will be able to play a more important role in the distribution of prime numbers, and even more extensive problems!

Finally, when the writing on the blackboard was about to be finished again, Xiao Yi stopped writing.

"Well... that's all we can do for now."

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 as he was about to speak to Faltings, he heard applause behind him.

"Incredible!"

"awesome!"

"Perfect!"

Xiao Yi was stunned.

He turned his head and saw three uninvited guests who had entered the room at some point in time.

Four people surrounded him.

To be more specific, four Fields Medal winners surrounded him, an underage boy.

"Uh, professors..."

But before he could say hello, Bombieri asked hurriedly, "What's your next idea?"

(End of this chapter)