The full name of the circle method is "Hardy Littlewood circle method", which is not only an important tool for studying Goldbach's conjecture, but also an important tool often used in analytic number theory.

And about the invention of this tool, it is not in the Goldbach problem. It is now generally accepted in the mathematical community that this concept first appeared in Hardy's work with Ramanujan on the "Asymptotic Analysis of Whole Number Splitting" problem, and was later completed when Hardy and Littlewood collaborated on the Warring problem.

Today, as an important tool for studying Goldbach's conjecture, this tool has been carried forward by later generations of mathematicians.

For example, Helfgort standing on the podium is a great star in the circle theory of number theory today.

“…… Goldbach's conjecture is that any even number greater than 2 can be written as the sum of two prime numbers, which we call conjecture A. ”

“…… Since the odd number minus the odd prime is an even number, and conjecture A argues that any even number is equal to the sum of two prime numbers, so conjecture A can be used to infer conjecture B that any odd number greater than 9 can be written as the sum of three odd primes. ”

At this point in the opening remarks, Herbgort paused and continued.

"And the 'circle method' I am talking about is the weak conjecture that proves his Goldbach conjecture, that is, conjecture B!"

Conjecture A is true, and Conjecture B must be true.

But not the other way around.

As for why, this involves an interesting question in logical mathematics. It is difficult to describe in elementary mathematics, but in descriptive language, the set of "the sum of any odd number and odd prime" greater than 9 is not equivalent to the set of "any even number", and all the elements in the intersection are infinite, and cannot be exhaustively proved.

In fact, from an abstract point of view, whether it is the "even number set" of the circle method or the "1+1 form" of the sieve method, everyone is half a catty and eight taels, and they are all short of the last kick.

This distance may be across a river, or it may be two mountains facing each other.

After a brief opening remark, Helfgot didn't talk nonsense and wrote a line of equations on the board.

【…… When 2||N, there are r3(N)=1/2n(N²/N³)∏(1-1/(p-1)²)∏(1+1/(p-1)²),(1+O(1)))]

The moment he saw this line of calculation, Lu Zhou's eyes lit up slightly.

This line of expression is not just a random copy of the old gentleman, but one of the many expressions proposed by Hardy and Littlewood, the big men in the field of two-digit number theory, in that paper in 1922!

When studying the twin prime conjecture, Lu Zhou happened to consult that document and even cited some of its conclusions.

It is precisely because of this that he can be said to be impressed by this.

It seems that this report will be a bit interesting.

The old man standing in front of the whiteboard did not say a word, and continued to write with a marker.

There was silence in the venue.

Not only Lu Zhou listened very seriously, but even the other bigwigs listened very seriously.

There is a specialization in the art industry, and even if it is a big guy, it is impossible to go deep into other people's fields in an instant. Therefore, the papers in the general report meeting will be released in advance on the official website of the conference for people to preview, and the questions to be asked will be written in the notes.

If the report does not answer your own questions, it is the right posture to listen to the academic report in the question session, and it is not just a matter of watching the excitement and applauding to participate.

More than forty minutes passed, and Helfgot stopped the marker in his hand and turned to look at the venue.

"That's the basic proof process, if you have any questions, you can ask them now."

Lu Zhou raised his hand.

Helfgot and Lu Zhou looked at each other, nodded, and motioned for him to get up and speak.

Glancing at his notes, Lu Zhou stood up and asked.

"I have questions about the equation you came up with in row 34. In your operation on =∑a(n)z^n+δ(n), you directly get each integer n>0. I'm guessing you're probably using the Cauchy-Gusa theorem or its corollary number theorem. But how do you tell if the function f(s) is a pure function? ”

There was a whisper in the venue.

Obviously, the question asked by Lu Zhou has touched the hearts of many people.

"That's a good question," Helfgo glanced at Lu Zhou deliberately, turned around and wrote a line of equations on the whiteboard, and then tapped a marker on it, "Got it?" ”

Seeing that line of calculations, Lu Zhou's expression was slightly abrupt and he nodded.

"Understood, thanks."

Nodding politely, Lu Zhou sat back and copied the supplementary equation on the whiteboard in his notebook.

Although his research was mainly on sieve methods, Mr. Wolfgot's methods were also very instructive for his research work. The so-called research work is exactly like this, refining one's own theories in exchanges and discussions, and rubbing new ideas in the collision of ideas.

Just as Lu Zhou was sorting out his notes, someone next to him gently poked his arm.

"I'm sorry, can I ask you a question?"

It was a little girl with a slightly pale complexion and slightly curly blonde hair.

The reason why she is said to be a little girl is because she doesn't look very old, a little shorter than Lu Zhou, and she is probably an undergraduate student at UC Berkeley...... If you want to say that she is a graduate student, Lu Zhou will never believe it anyway.

Although her English pronunciation is a little jerky, her voice is very soft and surprisingly a little nice.

No matter whether the voice is good or not, for Lu Zhou, if someone discusses mathematical problems with him, as long as it is not vexatious, he will never refuse, so he said generously: "Ask." ”

The girl blinked, pointed to the whiteboard with some embarrassment, and said, "I'm sorry, that...... What did you just understand? ”

When she saw that line of arithmetic, she didn't understand it at all.

"You're asking about that expression?" Probably guessed the question she wanted to ask, Lu Zhou patiently explained: "Because I(n)=∫{f(s)/s^(n+1)}ds=2πian in that line of arithmetic, this is a closed-orbit integral, so back to the original formula, you can directly use the remainder theorem." Professor Helgoft's explanation of the idea may be jumpy, and it is really difficult to understand, so think about it. ”

Listening to Lu Zhou's explanation, the girl took notes in her notebook in a panic.

Judging from her meticulous note-taking technique, Lu Zhou was even more convinced of her guess that she was probably an undergraduate.

But can you really understand this kind of lecture as an undergraduate?

Afraid that she would be embarrassed to ask, Lu Zhou said casually: "Do you have any questions?" ”

"Thanks, no more...... Excuse me, can you give me your email address? I still have a lot of questions to ask...... You. Because she was too nervous, this girl, who looked a little reckless, accidentally bit her tongue and turned red.

It can be seen that she is not very good at communicating with people.

is also not particularly good at communicating, Lu Zhou can understand, so he didn't care, and said casually: "It's okay." Plus, you don't have to say 'I'm sorry' all the time. My name is Lu Zhou, what is your name? ”

"I know your name is Lu Zhou, and I saw you at the opening ceremony," the girl added embarrassedly, probably remembering that she hadn't declared her name yet, "My name is Vera, and I'm studying at Berkeley...... He is interested in pure mathematics, especially in the direction of number theory. ”

Vera?

Sounds a bit like Hebrew, Russians?

Lu Zhou subconsciously glanced at her chest, although it was not as flat as a horse, but it was indeed a little shabby.

emmm……

Probably not, right?

"How old are you?"

“17……”

Lu Zhou glanced at her in surprise: "Can you go to Berkeley at the age of 17?" ”

At this age, he hasn't graduated from high school yet.

"I'm an IMO gold escort......" Vera smiled embarrassedly and said in a somewhat admiring tone, "Of course, it's not worth mentioning compared to you who have already solved two mathematical conjectures......"

Lu Zhou was stunned for a moment and said, "...... No, the gold medal in the Mathematics Olympiad is already strong, and you can be confident and don't be presumptuous. Surprisingly, you won a gold medal at the age of 15? So what age did you go to high school—"

At this moment, the last questioner finished speaking, and seeing that no one continued to ask questions, Mr. Hurfgot, who was on the stage, declared the report closed.

"We still have a long way to go in terms of fully proving the Goldbach conjecture."

"That's all for my presentation, thank you for being there!"

Helfgot nodded slightly, and walked off the stage amid applause.

Because he has not participated in the IMO competition, Lu Zhou is still quite interested. Originally, he was going to have a few words with the little girl who won the gold medal, but seeing that the time was not early, and it happened that he still had something to do, he put this matter aside, packed up his notes, and walked outside the venue.