Scholar’s Advanced Technological System

The full name of the round method is "Harday Redwood Round Method", which is not only an important tool for studying Goldbach's conjecture, but also an important tool often used in analytical number theory.

The invention of this tool is not on the Goldbach issue. It is now widely believed in the mathematics community that this concept first appeared in Hardy’s research on the “asymptotic analysis of integer splitting” with Ramanukin’s research, and then when Hardy and Littlewood collaborated on the Hualin issue. , was added to complete.

Today, as an important tool for studying Goldbach's conjecture, this tool has been promoted by later mathematicians.

For example, Helfgott standing on the podium is the big cow of the theory of round law in the field of number theory.

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

"... Since the odd number minus the odd prime number is an even number, the guess a considers that any even number is equal to the sum of the two prime numbers, so the guess can be obtained by guessing a, and any odd number greater than 9 can be written as the sum of three odd primes. ""

The opening remarks came here, and Helf Gottton paused and continued.

"And the "circle law" I am talking about is the weak conjecture that proves his Goldbach conjecture, that is, guess b!"

Guess a is established, guess b must be established.

But the other way around, but not.

As for why, this involves a very interesting question in logical mathematics. It is difficult to describe in elementary mathematics, but in a descriptive language, it is a set of "the sum of odd and odd primes greater than 9", which is not equivalent to the set of "any even numbers", and is in the intersection. All elements are infinite and cannot be proved exhaustively.

In fact, from an abstract point of view, whether it is the "even set" of the round method or the "1+1 form" of the sieve method, everyone is half a catty, and the difference is the last one.

This distance may be separated by a river or by two mountains.

After a brief opening remark, Hulfgot did not talk nonsense and wrote a line of calculations on the whiteboard.

[...when 2n, there is (n)=1/2n(n2/n3)n(1-1/(p-1)2)n(1+1/(p-1)2), (1+o (1))】

Seeing the moment of this line of calculations, Lu Zhou’s eyes were slightly bright.

This line of expression is not the old gentleman's scribbled, it is the two-digit argument of Hardy and Littlewood, one of the many expressions presented in the paper in 1922!

When studying the twin prime conjecture, Lu Zhou just consulted the literature and even quoted some of the conclusions.

It is for this reason that he is very impressed with 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 no sound in the venue.

It’s not just Lu Zhou’s listening very seriously, even the other big ones are listening very seriously.

There is a specialization in the industry, and even if it is a big man, 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 write the questions to be asked on the notes.

If the report does not answer your own questions, ask questions in the questioning section. This is the correct posture for listening to the academic report. It is not just a matter of watching the excitement and taking the time to participate.

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

"The basic proof process is like this. If you have any questions, you can ask questions now."

Lu Zhou raised his hand.

Helfgott and Lu Zhou looked in the line and nodded, indicating that he could speak up.

I took a look at the notes and Lu Zhou stood up and asked.

"I have doubts about the formulas listed on line 34. In the operation of =∑a(n)z^n+δ(n), you can directly derive each integer n>0. I guess the possibility you use. It is the Cauchy-Gusa theorem or its inference residue theorem. But how do you judge the function f(s) as a purely function?"

There was a whisper in the venue.

Obviously, Lu Zhou asked this question and asked many people's hearts.

"This question is very good," Herfgot accidentally glanced at Lu Zhou, turned and wrote a line on the whiteboard, and then the marker was knocked on it. "Do you understand?"

Seeing that line of calculations, Lu Zhou’s expression was slightly awkward and nodded.

"Understood, thank you."

Courtesy nodded, Lu Zhou sat back, and copied the line of the supplementary formula on the whiteboard to the notebook.

Although his research is mainly on screening, Mr. Herfgot's method is also instructive to his research work. The so-called research work is exactly the same, perfecting his own theory in exchange discussion, and rubbing new ideas in the collision of thinking.

Just as Lu Zhou was taking notes, someone next to him poked his arm.

"Sorry, can you ask a question?"

I spoke to a little girl with a slightly pale skin and a small blond hair.

The reason why it is a little girl, because she looks younger, is a little shorter than Lu Zhou, probably to increase the undergraduate students at Berkeley... If she is a graduate student, then Lu Zhou is absolutely unbelievable.

Although her English pronunciation is a little jerky, the sound is very light and the accident is a bit nice.

Regardless of whether the sound is good or not, for Lu Zhou, some people discuss math problems with him. As long as they are not unreasonable, he will never refuse, so he said very generously: "Ask."

The girl blinked, and some pointed at the whiteboard and said, "Sorry, that... what did you know?"

She didn't understand it when she saw the formula.

"You asked the expression?" Probably guessed the question she wanted to ask. Lu Zhou patiently explained: "Because i(n) = ∫{f(s)/s^(n+ in the calculation formula) 1)}ds=2πian, this is a closed-loop integral, so you can use the residue theorem directly when you return to the original form. Professor Hergoff’s explanation may be more leaping, really difficult to understand, think more ""

Listening to Lu Zhou’s explanation, the girl hurriedly recorded notes on the book.

From her ruthless note-taking technique, Lu Zhou was more convinced of her own guess, she was probably studying undergraduate.

But can the undergraduate listen to this kind of lecture really understand?

I am afraid that she is embarrassed to ask, Lu Zhou casually said: "Is there any doubt?"

"Thank you, no... Sorry, can you give me your email? I still have a lot of questions to ask...you." Because it was too nervous, the girl who looked a little rash, accidentally bite her tongue. The face is red.

I can see that she is not very good at communicating with people.

The same is not particularly good at communication, Lu Zhou can understand, so I did not care, casually said: "It doesn't matter. In addition, you don't have to always say 'sorry'. My name is Lu Zhou, your name is?"

"I know that you are Lu Zhou. I saw you at the opening ceremony." It may be that I suddenly remembered that I had not reported my name yet. The girl was embarrassed to add a sentence. "My name is Vera, I am studying at Berkeley... ...very interested in pure mathematics, especially in the direction of numbers."

Willa?

Sounds a bit like Hebrew, Russian?

Lu Zhou subconsciously swept her chest, although it was not a flat, but it was really shabby.

Emmm...

Probably not?

“Try to ask, how old are you this year?”

"17..."

Lu Zhou looked at her strangely: "Is it 17 years old to go to Berkeley?"

At this age, he has not graduated from high school.

"I am an imo gold medal..." Vera was embarrassed to smile, and said with a bit of admiration, "Of course, compared with you who have solved two mathematical conjectures, it is not worth mentioning..."

Lu Zhou squatted and said: "... No, the gold medal in the Olympic Math Competition is already very strong. You can be confident and don't have to be arrogant. Surprisingly, you got the gold medal when you were 15 years old? Then you are a few years old. High school"

At this moment, the last questioner finished his speech and saw no one continued to ask questions. Mr. Helfgott on the stage announced the end of the report.

"We have a long way to go to fully prove the Goldbach conjecture."

"My report will be here, thank you for coming!"

Herfgot nodded slightly and walked down the stage in a round of applause.

Because he has not participated in the imo contest, Lu Zhou is still very interested. Originally, he also planned to talk to the little girl who got the gold medal, but it was not too late. It happened that he still had something to do. He put the matter aside, packed up the notes and walked outside the venue. go with.