From university academician to chief academician

Amata stood on the stage, looking at the dense crowd below.

He was a little excited, this was his stage, and here he was about to show his abilities to the world.

For the International Conference of Young Mathematicians, he showed great ability.

He has proved many conjectures and made significant contributions to BSD conjectures.

Today, he is going to come up with another conjecture, the Gaussian class conjecture.

He has been studying the Gaussian number conjecture for more than a year and finally proved it a month ago.

Compared with the conjectures he proved in the past, the Gaussian class conjecture is no easier than them.

In terms of importance, it is not weaker than them at all.

Gauss only made three conjectures in his life.

They are the Gaussian class conjecture, the Gaussian class conjecture in the imaginary quadratic field and the Gaussian class conjecture in the real quadratic field.

These three conjectures are combined into the Gaussian conjecture.

Gauss's conjecture was proposed in the middle of the seventeenth century, about two hundred years ago.

For about two hundred years, the world has been studying Gauss's conjecture.

And so far it has not been proven.

Moreover, as the prince of mathematics, Gauss's conjectures were very high in terms of difficulty and importance.

And today he proved to the world the first conjecture of Gaussian conjecture, Gaussian analog conjecture.

As for the fight with Balazs, he didn't care.

In his opinion, there was no competition between them.

It's just an academic crash to prove the same issue.

And this happens all the time in academia.

There are only so many conjectures, and many people will study them. It is very likely that many people will study the same conjecture.

Therefore, strictly speaking, it is not a competition between them.

But something inappropriate happens at an inappropriate time.

Completely by chance!

Amata said: "Suppose the positive integers d1 and d2 satisfy gcd(d1, d2)=1..."

As he spoke, he wrote a set of formulas on the whiteboard behind him.

At the same time, the content on the whiteboard is displayed on a large display screen hung on the wall.

This way everyone in the room can see it.

"good!"

Many people present nodded, including some academicians and fellows.

Their vision and wisdom are much higher than those of the young mathematicians present.

Amata’s proof idea can be seen at a glance.

Academician Wei said to a middle-aged white man with curly white hair next to him: "Amata used the generalized Ramanujan-Nagell equation and the Lucas/Lehmer sequence in the Gaussian class conjecture."

"Yeah!" Lyle, who was beside Academician Wei, said, "That's true. It's a very novel idea."

"His research can be used in cryptography."

Because Amata used ideal groups in his paper.

It is common knowledge in mathematics that ideal groups establish a secondary domain cryptosystem.

The smartest thing about Amata is to use the quadratic domain cryptography system to find ideal subgroups of large prime order for the ideal class in the quadratic domain, and to study the divisibility of class numbers.

Although this idea has been mentioned before, few people have applied it to Gaussian number conjecture as naturally as he did, which also made everyone's eyes light up.

Amata said: "Consider the Diophantine equation d1x^2+d2y^2=4p^z..."

"Equation (6.1) has at most one solution with some known exceptions. These two theorems are proved."

"This is the Gaussian class conjecture."

"Bah bang bang..." Everyone applauded warmly.

"As expected of Amata, wonderful!"

"Yeah, I don't know if Balazs will be able to give such a wonderful academic report in the future."

"Very good, very good, really a wonderful academic report."

"With such academic ability at this age, he will definitely be one of the top international mathematicians in the future."

"..."

Many people sighed with emotion.

There are also many people who envy Amata’s mathematical talent.

There are also many people who envy that there are mathematician geniuses like Amata in England.

Among them were many Xia mathematicians.

Academician Wei sighed with emotion: "What a genius in number theory. Why don't we in the Number Theory Association have such a genius?"

"Hey..." Academician Wei sighed helplessly: "Our country still has a long way to go in cultivating talents!"

Due to the large population, Xia State could only adopt exam-oriented education.

But exam-oriented education has a big drawback.

Good at taking exams, but not good at innovation and practical skills.

Many need inspiration, inspiration and innovation are one thing.

A person who is good at taking exams but not good at innovation will not go far in mathematics.

Therefore, it is difficult to cultivate academic talents through examination-oriented education.

Unless this person is very talented.

Academician Wei gathered his mood, feeling sad and regretful, nothing could be changed.

Exam-oriented education is a national policy, and the national policy needs to serve the majority of people, not a small group of people.

He continued to read academic reports.

Next up was Amata answering questions from the audience.

After about half an hour, Amata's academic report ended.

Next is Balaz’s academic report.

Everyone is very interested in the academic reports of both of them, and they all want to know who is stronger and who is weaker between the two of them on the same academic report topic.

Balazs walked onto the stage. He knew before attending the International Conference of Young Mathematicians that Amata's academic report was on the same theme as his.

He is not interested in competing with Amata.

Whether Amata is strong or weak, it has no effect on him.

There are always people who are better than him in this world. If he always thinks about competing with others, then his life will be very tiring.

Therefore, he only competes with himself.

Balazs said: "Suppose D is a positive integer without square factors, h(-D) is a Gaussian number, Q(-D) is a number..."

Academician Wei nodded in agreement: "Balaz's academic report is also very good, not inferior to Amata's at all."

"Lyle." Academician Wei looked at Lyle beside him and asked, "What do you think?"

"His ideas are also very novel." Lyle said: "He uses the basic factors of Lucas numbers."

"In the past, the basic prime factors of Lucas numbers were used to solve Diophantine equations. It was rarely used to prove the Gaussian number conjecture."

"And like Amata, he also used the basic prime factors of Lucas numbers to self-justify the Gaussian number conjecture."

"His views give us more ideas in proving Gaussian conjecture."

"Yes!" Academician Wei nodded: "That's true."

"Hey..." He shook his head and sighed: "Amata and Balaz are both very good."

"To use our Xia country's idiom, their abilities are between equals, no matter how high or low they are."

Lyle nodded and said: "That's true. From the perspective of number theory research among the young generation in the world, these two are the best."

"Yes!" Academician Wei nodded.

Academician Wei felt very sorry that these two people were not from Xia.

He thought to himself: "It would be great if I were from the Xia Kingdom. Such number theory geniuses are rare!"

"It would be great if our Xia country had such a genius."

Facing such talents, Academician Wei was very itchy.

I can't wait to let them enter the Xia Guo Number Theory Association.

Of course, this is unrealistic.

One of them is from Beili, and the other is from England.

Mathematics in these two countries is better than that of Xia Guo. It is impossible for them to enter the Number Theory Association of North Korea and the Number Theory Association of England, but it is impossible for them to enter the Xia Guo Number Theory Association.

Academician Wei was a little depressed, but he soon regained his composure.

Since you can’t force it, then you don’t want to.

It is better to seek help from others than to seek help from yourself. Think about how to cultivate people in your own country!

Maybe we can find a number theory genius.

He thought to himself: "That's Ye Fei down there!"

Song Chengkun looked at Ye Fei and said with a smile: "It's you next, don't be nervous, take it easy."

Ye Feidao: "I'm not nervous!"

"Are you really not nervous?" Song Chengkun looked at Ye Fei suspiciously: "Don't hold on!"

"I'm not nervous at all." Ye Fei shook his head: "It's not your first time to give an academic report on stage. What's there to be nervous about?"

"The two people in front of you are so strong. Aren't you afraid that your speech will not be as good as the two in front of you and the audience will complain about it?"

Ye Fei smiled and said: "I'm not afraid, I won't be complained about."

"Why are you so confident?" Song Chengkun rolled his eyes.

The three of them all talked about the same academic report topic, and the order of taking the stage was still close to each other.

The first two people spoke very well. If Ye Fei spoke poorly, everyone would be able to tell.

When the time comes, the audience will complain, and it will be about who is weak and who is embarrassed.

Ye Fei's eyes flashed with light and he said: "Because of confidence."

If he had not read the academic reports of Amata and Balazs, he would still doubt himself and be a little nervous.

But after reading the two people's academic reports, he knew that he was sure.

Ye Feixin said: "These two people look at their resumes and think they are very powerful, but in fact they are just like that."

Again, the problems Ye Fei proved were not comparable to them in quantity, but they were higher in quality.

"I seek quality, not quantity."

After half an hour, Balazs finished his academic report after taking questions from the audience.

Ye Fei stood up from his seat and took a deep breath.

Song Chengkun clenched his fists, cheered Ye Fei up, and said, "Ye Fei, come on!"

Ye Fei smiled at him, then strode towards the stage.

The audience was still discussing Balaz's academic report just now, and few people paid attention to Ye Fei.

Ye Fei walked onto the stage and said: "Hello everyone, I am Ye Fei from Zhonghu University. The content of my academic report is the Gaussian class conjecture."

"Uh..." Many viewers were shocked when they heard Ye Fei's words.

Although car crashes are common in academic reports, this is too common!

The three people all gave academic reports on the same topic, and the order of the three academic reports was still close to each other.

But who is this Ye Fei!

The first two are Amata, the son of a Fields Medalist, and Balaz, a student of the Fields Medalist.

This Ye Fei is from Xia, and he is from a little-known university, so he should have nothing to do with the Fields Medal winner.

Such people are not looking for abuse when they give academic reports on the same topic as Amata and Balazs!

At this time, many people were either amused or pitiful.

Yuan Zhengsong and the others sighed in their hearts: "Hey... I hope Ye Fei can survive it!"

Ye Feidao: "I combined the Gaussian class number conjecture with the Eisenstein series and the Riemann function to explore the class number 1."

"Huh?" After hearing Ye Fei's words, many people perked up.

What he said seemed interesting.

Eisenstein series is a type of modular form that can be directly expressed as a series. This is a formula for studying the Riemann Hypothesis.

But in the past, no one had combined the Eisenstein series with the Gaussian class conjecture.

Although the Gaussian class conjecture is closely related to the Riemann hypothesis.

The Eisenstein series is also related to the Riemann Hypothesis.

But the Eisenstein series has no connection with the Gaussian class conjecture.

It's like A and B are father and son, and C and B are friends, but there is no connection between A and C. It is because of B that they seem to be connected, but in fact they are still not connected.

Ye Fei wrote a set of formulas on the whiteboard behind him.

[x(1)=1

…

x(n)=0 if gcd(n, N)\u003e1】

Ye Feidao: "Suppose N is a positive integer and x is a Dirichlet character modulo N. For all integers m and N..."

"..."

"Where x is the Dirichlet function, let f(T) represent (T, P) represented by x."

"Wow..." The audience exclaimed, and many people said in surprise: "He really combined the Gaussian class conjecture with the Eisenstein series and the Riemann function."

"God, how did he think of that?"

"Oh my God, it turns out this can be explained."

One academician said excitedly: "He made good use of the Riemann function as a link and combined the Gaussian class conjecture with the Eisenstein series."

"What a genius idea."

"This man named Ye Fei is really a genius in number theory."

"He's a bigger genius than Amata and Balazs."

"Although Amata and Balaz's academic report is very exciting and has bright spots, their ideas have been mentioned before."

"And this person named Ye Fei, his ideas have never been mentioned before."

"And, now it seems that Ye Fei's idea is more concise than Amata's idea to prove the Gaussian number conjecture."

"If Amata and Balaz are geniuses, then Ye Fei is a genius."

Many people in the audience were as excited as if they had discovered a new world, and their eyes lit up when they looked at Ye Fei.

Those who knew Ye Fei were shocked.

Academician Wei looked at Ye Fei dumbfounded. He had not come into contact with Ye Fei before the International Conference of Young Mathematicians, so he did not know Ye Fei's ability.

But he heard the president say that Ye Fei was a genius.

However, there were too many geniuses in the mathematics world, and he thought Ye Fei was just an ordinary genius.

But now it seems that this is not an ordinary genius, it is simply a genius!

Lyle asked Academician Wei beside him: "Is this Ye Fei from your Xia Guo Number Theory Association?"

"Yeah!" Academician Wei nodded blankly.

Lyle said with envy: "Your Xia Guo Number Theory Association has such a genius and wants to produce a top number theorist."

Academician Wei didn't know what to say. The surprise came so suddenly that he was caught off guard.

Song Chengkun looked at Ye Fei in surprise. Ye Fei was actually more talented than Amata and Balaz.

He said before that Ye Fei was inferior to these two people, but now he felt a little ashamed.

How could this be inferior to these two people? They were simply pressing them to the ground and rubbing them.

Amata and Balaz were even more shocked. They thought that the International Conference of Young Mathematicians was a competition between them.

Unexpectedly, a person suddenly jumped out. The theme of his academic report was exactly the same as theirs, and he completely defeated them.

This...this is really unbearable!

Then, the two of them were excited, as if they had a tacit understanding, and they had the same idea at the same time.