From Almighty Scholar to Chief Scientist

Chapter 87
Mathematician Eichler once said that there are only five basic operations in mathematics, addition, subtraction, multiplication, division, and modular forms.

Perhaps this is a very personal argument, but it does show that modular forms are ubiquitous in today's deeper mathematics.

The modular form is an analytical function, and this function will become a certain type of functional equation under a group operation of the model group, and the value calculated by the function will also show a certain growth trend.

All in all, this is a mathematical tool with a wide range of applications, including the Taniyama Yutoshi-Shimura Goro conjecture in the process of proving Fermat's Last Theorem, and also uses modular form theory.

Research on the connection between modular form theory and group theory also exists widely in the mathematical community.

At this moment, Lin Xiao saw such an application in the proof process of Professor Selberg in front of him.

"Yeah, why didn't I think of that?"

While absorbing the knowledge in these manuscripts as if he had been enlightened, he felt the enlightenment brought to him by the knowledge in it.

As expected of Professor Atle Selberg, who once proved the prime number theorem, this kind of application of knowledge is truly worthy of the master's masterpiece.

"After studying group theory and Li groups for so long, I couldn't think of such a change. In this way, I can match my previous steps..."

Lin Xiao's eyes became brighter and brighter.

Then he quickly picked up the pen and scratch paper, and started the next interpretation.

These manuscripts did not tell him the answer. After all, Professor Atle Selberg did not succeed at the beginning, so he needs to follow the ideas conveyed in the manuscripts to complete the next work.

And the next job is a big project. He needs to combine group theory and his previous research, and then integrate modular form theory into it to complete a new mathematical method with more applicability.

And through this new method, he had a hunch that he would be able to accomplish his ultimate goal.

However, he had to try to know, after all, sometimes inspiration can also become an illusion.

Even the original Professor Selberg only used this method in it, but in the end it was not and did not succeed.

Of course, having a direction is the most important thing for mathematical research.

So, Lin Xiao continued his work.

【……F2k(τ)=(2ζ(2k))^(-1)G2k(τ)，τ∈H.
……

log|P(ζ1，ζ2，ζ3)|>-μT^4(logT)^24……】

Lin Xiaoyue writes, the more he feels that his thoughts are springing up, although this does not allow him to find the state where the brain development rate reached more than 4% in the sage state, but this state of continuous inspiration is also commendable.

Even if he encounters certain problems in the middle, he can still solve them quickly.

In this way, with the listing of formulas line by line, and the continuous combination of piles of English letters, Arabic numerals, and Greek letters, pieces of draft paper were used by him, and some were thrown aside by him. , and some were kept by him.

Time passed.

He could already feel that he was getting closer to the final result than ever before.

After an unknown period of time, Sun Yu, Ouyang Sheng and others who also finished the exam have also returned with the two team leaders. When they saw Lin Xiao's closed room, they all shook their heads and did not bother.

"I don't know if Lin Shen can solve that problem."

"Since everyone calls Lin Shen, all you need to do is believe in God."

"In the future, I will have to make a memorial tablet for God Lin and offer it at home every day. I just hope that I can be half as good as him."

"Half awesome? You're afraid you want to go to heaven."

Several people laughed and joked, then continued to review their exam process and answered the questions correctly.

However, all in all, they all felt pretty good in this exam, and they performed fairly well. Except for the third and sixth questions, which were the final questions, which they found very difficult, they still had a certain degree of confidence in the other questions.

In this way, they chatted until the afternoon, and stopped by for a meal in the middle. As for Lin Xiao, although they did not have dinner with them, they still helped Lin Xiao bring food back. When they entered the research state and couldn't take care of eating, they all brought the food for Lin Xiao.

Until the evening, they began to plan to go out for supper, to make up for the regret that they could only eat in the hotel these days, and by the way, they could also experience the local customs here.

However, just as they were about to go out, the closed door was opened, and Lin Xiao walked out from inside.

"Hey, Lin Shen, it's a coincidence that you came out, we were just talking about going out."

"Going out to eat?" Lin Xiao asked.

"correct."

"Then go." Lin Xiao rubbed his stomach and said awkwardly, "I'm a little hungry."

"My God, Lin Shen still feels hungry!"

"Then hurry up, how can you make Lin Shen hungry?"

This group of people immediately yelled and pulled Lin Xiao when they came up, and then they were about to set off.

Seeing them like this, Lin Xiao shook his head helplessly.

From 10:30 in the morning to around three o'clock in the middle, he only ate a Romanian specialty cabbage roll and a small plate of cannelloni that they brought back. It is already ten o'clock now, and he is really happy hungry.

This is also a rare situation where he was directly starved out of the immersion state.

Of course, after such a long period of research, he has achieved remarkable results. Although he has not yet succeeded, he can basically be sure that his direction is correct. As long as he continues to walk, success is already a visible direction.

However, people are iron rice or steel, let's fill up one's stomach first.

Afterwards, Lin Xiao left the hotel with them, went out to eat supper, and admired it.

…………

The next two days are the time for the IMO test paper marking team to correct the test papers. At the same time, each contestant is also organized to go on an excursion.

However, Lin Xiao, who was devoted to his own problem, did not participate in this activity, but continued to do research in the hotel.

Finally, until July 7th, his research came to an end.

Looking at the final long series of formulas in front of him, Lin Xiao looked back at the previous process, and finally let out a sigh of relief: "So, it's finished."

"So, should I call it Lin's group transformation theory, or Lin's modular form transformation method?"

"Hey, forget it, don't worry about this for now, let's get the last problem done first."

The final question is the distribution law of Mersenne prime numbers.

At this moment, for him, the answer that was so far away from the chasm was already at his fingertips.

(End of this chapter)