Zhao Tian laughed dryly: "Hehe, study and play." ”

"Then let's work together. Ou Ye walked over to the blackboard and carefully observed the deduction on the blackboard.

"Sister Ye Zi sits. Zeng Han pulled the chair and rested it behind Ou Ye.

"Hmm. Oye sat down.

"Sister Ye Zi drinks water. Xiaoyun poured a cup of hot water and handed it to Ou Ye.

"Thank you. Ou Ye took the water cup and didn't drink it, just warmed his hands.

Tick tock, time passes.

Ouye didn't speak, and the three students were silent.

That's probably how they did it.

After a long time, Ou Ye asked, "Xiao Zhao Baoyan has come to our academy, right?"

Zhao Tian nodded again and again: "Yes, yes, I really want to choose Sister Ye Zi as my master's tutor, but Sister Ye Zi, you don't have students recently, so I can only choose Professor Liu." ”

"Oh, Professor Liu is a good teacher, he has a knack for group theory. Ou Ye said, and she turned to ask the other two, "What are your two GPAs?"

Zeng Han and Xiaoyun said in unison: "4.0." ”

"Oh, excellent. "Although there are not many members in the club where Ou Ye is the instructor, all the members are the elite among the students.

After a brief chat, Ouye stopped talking again, and she focused on the mathematical symbols on the blackboard.

A teacher, three students, just quietly looked at a blackboard.

After a long time, Ou Ye stood up, she erased the chalk words on the blackboard, leaving only a lonely line of words: E(Q) is the sufficient and necessary condition of the infinite set, L(E,1)=0.

To prove this sentence is to prove the BSD conjecture.

But in fact, "E(Q) is an infinite set of sufficient and necessary conditions L(E,1)=0" is not the form in which Birch and Swinnaton-Dale first proposed this conjecture, and their initial assumptions are mathematically stronger than this sentence, the so-called strong BSD conjecture.

The content of this line on the blackboard is a weak BSD conjecture, and the three students are in their hearts, Sister Ye Zi has found a breakthrough in the weak BSD conjecture?

Below the weak BSD conjecture, Ouye continues:

L(E,s) = c(s-1)^r + higher-order terms

It is clear which is stronger and which is weaker, but of course the following equation is stronger, and it is an expression of the strong BSD conjecture.

Whether strong or weak, it is not difficult for the best students in the mathematics department to understand the BSD conjecture, but it is difficult to prove.

Ouye hesitated for a moment, and finally erased the weak BSD conjecture and left the strong BSD conjecture.

"Let's do this. Ou Ye tapped on the blackboard.

"Sister Ye Zi, what does this mean?" Zhao Tian asked.

Ouye: "Prove it." ”

"Proof strong BSD conjecture?" Zhao Tian was stunned.

Ouye: "Yes, we prove it. ”

"Sister Ye, what do we mean?" Xiaoyun asked.

Oye: "You, you, and you, plus me." ”

"Sister Ye, you're really playing!" Zhao Tian thought he had heard it wrong.

Ou Ye was puzzled: "You guys, are you playing fake?"

Zhao Tian was a little incoherent: "I...... I'm ...... As I just said, it's a joke for us to study the BSD conjecture! Let's just say me, I've also studied P vs. NP, and I'm sure Professor Shen has also studied these problems, and studying it doesn't mean that we have to prove it...... We just watched it, and didn't think about conquering it. ”

Zeng Han, who had not spoken, suddenly spoke: "Senior Brother Zhao has already taken up the study, Senior Sister Yun and I usually have nothing to do, it is better to follow Sister Ye Zi and learn the skills to prove the strong BSD conjecture." ”

easily brushed the grade point to 4.0, and was not interested in falling in love, Zeng Han and Xiaoyun usually had nothing to do, so Xiaoyun got a Hong Kong and Macao pass, and Zeng Han wrote blackboards and erased blackboards here every day, pondering various academic problems.

Ou Ye stared at Zeng Han, this thin and tall big boy who didn't smile seemed to have the calm and calm temperament of a science student compared to Zhao Tian, who was babbling.

Being stared at by Sister Ye so bluntly, Zeng Han was a little uncomfortable, he smiled shyly, and the small dimples on his cheeks loomed.

In an instant, Ou Ye said: "Xiao Zeng, I remember you, you are the genius child who was sent to Yan University at the age of 15. ”

"I don't dare to call myself a genius, I just know how to do questions. Zeng Han scratched his head, looking stupid.

"You're not an adult this year, are you?" asked Ouye again.

Zeng Han said: "I am a few months away from turning 18 years old. ”

"It was great. Ou Ye nodded.

I don't know if it's because it's great to escort Yanda at the age of 15, or because it's great to be under 18 years old, anyway, after being praised by Sister Ye, Zeng Han felt very happy.

Ou Ye tapped the blackboard again and said, "If you want to do it, just do it with me." If you don't want to do it, forget it. ”

Zeng Han was the first to say: "I'll do it with Sister Ye." ”

Xiaoyun then raised his hand: "I will also do it with Sister Ye." ”

The younger brothers and sisters have all expressed their determination, as a senior and the president of the Ouye Computer Club, Zhao Tian can't be indifferent.

Zhao Tian puffed up his chest and said, "Count me in!"

So on this ordinary day, a frail female mathematics professor with three undergraduates launched a formal attack on the BSD conjecture, one of the millennial problems.

Ouye is determined to solve the strong BSD conjecture, which is understandable.

Ouye needs assistants, which is also understandable.

It is understandable that the assistant is a doctoral student or a master's student.

However, Ouye's assistants were three undergraduates...... Well, there's a prospective master's student among them.

Even if Zhao Tian, a prospective master's student in the Department of Mathematics, is counted, Ou Ye's assistant is still not strong enough.

At least it seems.

What does Ouye think?

She's been watching all morning.

L(E,s) can be extended to a function that gives an answer to any complex number s, and calculus can be applied to this function. This means that L(E,s) can be expressed in terms of the famous Taylor polynomial.

So the strong BSD conjecture can actually be expressed as follows: E(Q) is an infinite set and the sufficient and necessary conditions are cr≠0, but for n=0,...... , r-1, each coefficient cn is 0, where r is the rank of E.

To put it another way, counting the number of zeros at the beginning of a Taylor polynomial provides a measure of how much the function is zero at the point in question.

So another way of saying the strong BSD conjecture is that the rank of E gives an accurate measure of the degree to which L(E,1) is zero.

The three undergraduates' "joking" on the blackboard has touched on the core of the strong BSD conjecture.

This is the conclusion of Ouye's observation.

Mathematics is such a thing, talent can be seen at a glance.

Zhao Tian, Xiaoyun, and Zeng Han may be vague in the big picture, but they are smart enough, talented enough, and focused enough on mathematics. The three students are not a little old, but they are not in love, and they think that mathematics is much more interesting than falling in love.

Near noon, Ou Ye said to the three students, "Let's go eat first, and gather here in an hour." ”