Chapter 78 Inspiration from Chatting

Hearing Professor Pompieri's words, Professor Chen Qiusheng was stunned again and asked again: "What are you looking for...Classmate Lin Xiao?"

"Yes, Lin-Xiao." Professor Pompieri nodded, repeated it in Chinese with a slight English accent, and then apologized with a smile: "Maybe I still don't know how to say your Chinese names."

"No, no, what you said is very standard." Professor Chen Qiusheng waved his hand, then turned to look at Lin Xiao next to him, and said, "Lin Xiao."

Lin Xiao had long heard the old professor calling his name, but he was very confused, what did the Fields Medal boss want to do with him?

He stood up and shouted: "Pompi...Professor Pompieri, I am Lin Xiao."

It was his first time talking to a foreigner in English. He was still not used to it, including names, but it was no problem to introduce himself.

Professor Pompieri looked at him, and when he saw Lin Xiao's young face, a smile appeared on his face, "Can I have a few words?"

Lin Xiao thought for a while, finally nodded and said, "It's my pleasure."

"Haha, excuse me." Professor Pompieri nodded.

Lin Xiao then stepped over Sun Yu and the others, and walked up to Professor Pompieri under their gazes.

Professor Pompieri stretched out his hand, and under the gaze of countless people around him, he stretched out his hand towards Lin Xiao and said, "Mr. Lin, I'm glad to see you."

"Just call me by my name."

"Haha, we don't need to say more about these things. I came to you not to worry about such things." Professor Pompieri waved his hand.

"I have read the May issue of "Annals of Mathematics" this year. In "Proof of the Existence of Infinitely Many Prime Numbers in the Fibonacci Sequence", you solved a problem that I had spent several months studying. So I’m here specifically to thank you for solving this regret for me!”

Lin Xiao couldn't help but be stunned. It turned out to be for that paper?

Isn't it just an "Annual Review of Mathematics"? Dozens of papers appear in it every year...

Ahem, this is a bit much.

He smiled and said modestly: "It's just luck. Compared with you, this achievement is still only insignificant."

"No, no, no, that's not trivial. How many people want to achieve your level of achievement?" Professor Pompieri shook his head with a smile and said, "Of course, if you just solve this problem, I would at most I will only express my gratitude to you in my heart, but the key is the method you used. I had considered it and studied it for a period of time, and I believed that this method could be successful. At that time, I also worked with Atler Serre Professor Berg bet me a dollar that I would succeed, but after several months of trying, I still didn’t succeed.”

"Well, you should know Professor Selberg, right?"

Lin Xiao nodded.

He wrote that paper, and of course he had to know about Professor Selberg.

Atler Selberg, a master in analytic number theory and winner of the second Fields Medal in 1950, completed the elementary proof of the prime number theorem, and Lin Xiao used the prime number theorem in his paper. .

Professor Pompieri said with a smile: "Now that you have succeeded, it has made up for my regret and proved that the direction I chose was correct."

Lin Xiao learned that there was such a deep-seated reason. He smiled and said, "It seems you can win back that dollar now."

Pompieri waved his hand: "That probably won't work. In one month's time, it will be the eleventh anniversary of his death, and the bets were all made more than thirty years ago. In addition, by then I will I will print out your paper and burn it to him on that day - this seems to be a traditional custom in China, but now the United States has also learned it."

Lin Xiao was stunned. Listening to Pompieri's words, he almost thought Professor Selberg was still alive.

"Feel sorry."

Pompieri shook his head: "Nothing to apologize for. If I burn your paper to him and he receives it in heaven, I believe he will be happy because he also studied this issue. Of course he It didn’t work out, and I lost $1, so neither of us owes anyone anything.”

"So that's the case."

Lin Xiao nodded, feeling quite interesting about their bet.

When Professor Pompieri talked about this former friend, he seemed to be interested for a moment, and then asked: "Do you know what method he wanted to use in the first place?"

"What?" Lin Xiao asked curiously, of course he didn't know.

"Modular formal theory! He expressed each prime number in the Fibonacci sequence, and then used lattice to represent these partially ordered sets, and then found the functions that were these lattice, and then he..."

Professor Pompieri said this as if he was familiar with all the treasures in his family.

However, what he didn't notice was that Lin Xiao was lost in thought while listening to his words.

Modular formalism?

As a function of lattice?

If he expressed the Mersenne primes in Mersenne numbers using a grid, wouldn't it be...

He had knowledge in this area, and at this moment he felt as if inspiration was bursting out in his mind. However, when he wanted to grasp this inspiration, it was fleeting.

This is because his knowledge of modular formalism is not deep enough.

As a category of analytic number theory, he had learned about modular formal theory in the books he studied, but the book didn't cover much about it, so he needed to know more.

At this moment, he had a vague guess in his mind that there was a key key, right here!

"Huh? Lin, what are you thinking about?"

At this time, Professor Pompieri saw Lin Xiao's appearance, stopped his narration, and asked.

Lin Xiao came back to his senses and said: "The modular formalism you mentioned has inspired what I have been studying recently."

"Oh? You are here to participate in the IMO competition. Do you still have time to study other new things?" Professor Pompieri became interested, "What are you studying?"

"I have now summarized the method in my paper, and then want to use it to solve the problem of Mersenne prime distribution. However, I have encountered some difficulties. Now I need to continue to develop this method. The modular form you mentioned The discussion helped me find some direction.”

"Is it actually a Mersenne prime?" Professor Pompieri was surprised for a while, and then said with a smile: "Then I hope you can bring some surprises to the mathematical world again."

"Oh, by the way, if you need it, for example, if you want to see Selberg's manuscript, I can send you a scanned version. His other manuscripts are stored in the Flint Library of Princeton University, but this part of the manuscript Because he didn’t get any results, he gave them to me before he died.”

Thanks to kirky for the 100 starting coin reward.

PS: We are preparing to put it on the shelves on April 1st, and we are ready to start selling it every day. I would like to ask for the first order on that day, and I would be very grateful.