I Just Want to Be a Quiet Top Student

Zhao Tian laughed twice: "Hey, just study and play."

"Then let's study together." Ouye walked to the blackboard and carefully observed the deduction formula on the blackboard.

"Miss Ye Zi, sit down." Zeng Han pulled the chair behind Ouye.

"Yes." Ouye sat down.

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

"Thank you." Ouye took the water glass and didn't drink it, but just warmed his hands.

Tick ​​tock, time passes.

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

Maybe that's how they do their research.

After a long time, Ouye asked: "Little Zhao Baoyan has come to our school, right?"

Zhao Tian nodded again and again: "Yes, yes, I really want to choose Sister Ye Zi as my master tutor, but Sister Ye Zi, you have no students recently, so I can only choose Professor Liu."

"Oh, Professor Liu is a good teacher. He is very good at group theory." Ouye said, and she turned to ask the other two: "What are your grade points?"

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

"Oh, excellent." Although there are not many members in the club where Ouye 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 and three students just quietly looked at a blackboard.

After a long time, Ouye stood up, and she wiped off the chalk writing on the blackboard, leaving only a single line: E(Q) is an infinite set and the necessary and sufficient condition is L(E, 1)=0.

To prove this sentence is to prove the BSD conjecture.

But in fact "the necessary and sufficient condition for E(Q) to be an infinite set is that L(E, 1) = 0" is not the form in which Burch and Swinnerton-Dell first proposed this conjecture. The assumptions they made initially Stronger than this statement in a mathematical sense, the so-called Strong BSD Conjecture.

The line on the blackboard is the weak BSD conjecture, and the three students are shocked. Did Miss Ye Zi find a breakthrough from the weak BSD conjecture?

Euler continued below the weak BSD conjecture:

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

It is clear at a glance which is stronger and which is weaker. Of course, the following equation is stronger, which is the expression of the strong BSD conjecture.

Regardless of whether it is strong or weak, it is not difficult for outstanding students in the mathematics department to understand the BSD conjecture, but the difficulty is to prove it.

Ouye hesitated for a while, and finally erased the weak BSD conjecture, leaving the strong BSD conjecture.

"Let's just do this." Ouye tapped on the blackboard.

"Sister Yezi, what do you mean by doing this?" Zhao Tian asked.

Ouye: "Prove it."

"Prove the strong BSD conjecture?" Zhao Tian was stunned.

Ouye: "Yes, we prove it."

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

Ouye: "You, you, and you, plus me."

"Sister Yezi, you are serious!" Zhao Tian thought he heard it wrong.

Ouye was puzzled: "You three, are you playing fake?"

Zhao Tian was a little incoherent: "I... I, I, I... What I said just now, the three of us researched BSD conjecture is just for fun! Just say me, I have also studied P vs. NP, I believe Professor Shen I must have studied these issues, and studying it does not mean that we must prove it... We just took a look at it, and never thought of conquering it."

Zeng Han, who had been silent all this time, suddenly said, "Senior Brother Zhao has already been admitted to the graduate school. Senior Sister Yun and I have nothing to do at ordinary times. Why don't we follow Sister Ye Zi and learn the skills of proving strong BSD conjectures."

He easily raised his grade point to 4.0, and he was not interested in dating. Zeng Han and Xiaoyun really have nothing to do, so Xiaoyun got a Hong Kong and Macau passport, and Zeng Han wrote and wiped the blackboard here every day, thinking about it. various academic problems.

Ouye stared at Zeng Han, this thin, tall and serious boy seemed to have the calm and calm temperament of a science student compared to the bluffing Zhao Tian.

Being stared at by Sister Ye Zi so straightforwardly, Zeng Han felt a little uncomfortable, he smiled shyly, the dimples on his cheeks were faintly visible.

In an instant, Ouye said: "Xiao Zeng, I remember you, you are the gifted child who was sent to Yanda University at the age of 15."

"I don't dare to be called a genius, I just know how to solve problems." Zeng Han scratched his head, looking silly.

"Are you still an adult this year?" Ouye asked again.

Zeng Han said, "I'm a few months away from turning 18."

"Great." Ouye nodded.

I don’t know if it’s because it’s great to be sent to Yanda University at the age of 15, or it’s great to be under the age of 18. Anyway, Zeng Han was very happy to be praised by Sister Ye Zi.

Ouye tapped the blackboard again, and said: "If you three want to do it, just follow me. If you don't want to do it, forget it."

Zeng Han was the first to express his opinion: "I will do it with Sister Ye Zi."

Xiaoyun then raised her hand: "I'll do it with Sister Yezi too."

The younger brothers and younger sisters have all expressed their determination. As the senior and the president of Ouye Computer Club, Zhao Tian cannot remain indifferent.

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

So on this ordinary day, a frail female mathematics professor led three undergraduates to launch a formal attack on the BSD conjecture, one of the millennium problems.

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

Ouye needs an assistant, which is also understandable.

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

However, Ouye's assistants are three undergraduates... well, one of them is a prospective master's student.

Even counting Zhao Tian, ​​a quasi-graduate student in the Department of Mathematics, Ouye's assistant is still not strong enough.

At least it seems so.

How did Ouye think about it?

She's been watching all morning.

L(E, s) can be extended into a function that gives an answer to any complex number s, and calculus methods can be applied to this function. This means that L(E,s) can be represented by the well-known Taylor polynomials.

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

A more intuitive way to describe it is that counting the number of leading zero terms in a Taylor polynomial provides a measure of the degree to which 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 "joke" of the three undergraduates on the blackboard has touched the core of the strong BSD conjecture.

This is Euler's observation.

Mathematics is such a thing that one can see talent at a glance.

Zhao Tian, ​​Xiao Yun, and Zeng Han may be vague in terms of the overall situation, but they are smart enough, talented enough, and focused enough on mathematics. The three students are older, but they have never fallen in love. They think mathematics is much more interesting than falling in love.

Near noon, Ouye said to the three students: "Everyone go to eat first, and gather here in an hour."