Chapter 307 is the proof?
Xu Qingzhou grinned, took a deep breath to refresh himself, and said, "Okay, senior brother, I'll take a shower first and then go over."
"I'll wait for you in the lobby downstairs." Su Kewei was a little worried. He felt that Xu Qingzhou seemed very tired. If he neglected to be late, he would inevitably leave others speechless.
Xu Qingzhou nodded and took a shower with clean clothes.
The sound of running water soon sounded in the bathroom.
In the room, there was a breakfast plate on the dining table. You should have asked the waiter to deliver breakfast directly.
A corner of the desk was filled with discarded manuscripts, and the table was also covered with manuscript paper.
Outside the window, the weather was sunny and windy. The bright sunshine filtered in through the window and sprinkled on a corner. The breeze blew the curtains and raised the corner of the manuscript paper pressed by the cup on the desk.
If someone looks carefully, they can find something like this:
[On γ(T)|F(s)|=|xs+1s(s+1)(ζ′(s)ζ(s)|t|2|t|2=Axc+1|t|22< br>
It is easy to prove that ∫(Re(s)=c)+γ(T)F(s)ds=0. 】
[Let h1 [That is: for all natural numbers k, there are infinite pairs of prime numbers (p, p+2k), and the Polignac conjecture is proved. 】 That's right, after three days of hard work, Xu Qingzhou proved Polignac's conjecture. Although he was temporarily out of the control of Song School Belle, he was still not at the point where he often stayed up all night. In the past few days, he went to bed at 2 o'clock and got up at 6 o'clock in the morning. Just stayed up all night last night.
With a world-class result right in front of me, I couldn't sleep at all. After spending one night, he had gone through all the proof processes three times. Although some parts can be streamlined slightly, the logic is correct and the proof is correct. Next, I checked the calculations a dozen times, looked for bugs, and then announced the results. 9:25. After taking a shower, Xu Qingzhou finally felt much more awake. He changed his clothes, took the USB flash drive and documents needed for the report meeting, and went downstairs to find Su Kewei. Seeing Xu Qingzhou coming down, Su Kewei put away his notebook, and the two of them left the hotel and headed towards the lecture hall. Su Kewei asked curiously: "Junior brother, is the progress of Polignac's conjecture going smoothly?" "It's done." "Oh, it's okay, we are one after all." Su Kewei originally wanted to comfort this junior brother, but he stopped suddenly and looked at Xu Qingzhou in shock: "You said you proved it?!" "The proof came out." "Did you prove the Polignac conjecture?!" "Yeah." At 9:50, Xu Qingzhou arrived at the reporting hall, contacted the staff, and prepared to go on stage. There were many acquaintances in the lecture hall, including Professor Qin Yizhen, Chairman Cai Xinyuan, and Chairman Mori Chongwen of the International Mathematical Union. There were quite a few people. Most of them were experts in the field of number theory. There were also scholars who had studied number theory, or they were just joining in the fun.
Su Kewei was in a daze, looking for Professor Gu in the crowd. Damn, junior brother has killed another world-class guess! He wanted to report this matter to Gu Zhizhong, but found that Professor Gu was holding a manuscript and discussing the Selberg formula on arithmetic sequences with Academician Chu, and immediately planned to wait. 4 minutes passed. "Well, then by repeatedly using the properties ∑n≤x(n,k)=1f(n)=∑.d|n,d|kμ(d) and appropriate transfer terms, we can get the formula, we get, Lao Chu, come down and talk, let’s listen to this guy’s report first.” "Hehe, okay." Chu Jiangfeng smiled and nodded. Gu Zhizhong finished here, turned around, and found Su Kewei in a daze. "Xiao Su." "Professor." Su Kewei came back to his senses and finally remembered to tell his junior brother's awesome deeds. "Xiao Su, aren't you also very interested in the sifting method? You can discuss it more with your junior brother." "Yes, I remember, Professor" Gu Zhizhong waved his hand and said: "Let's talk about other things and listen to the lecture first." Su Kewei hesitated to speak. Seeing that Gu Zhizhong's eyes were already looking at Junior Brother Xu on the stage, he sighed helplessly, "Well, Junior Brother Xu should say it himself." At 10 o'clock, the report officially begins. "The main content of this report meeting is twofold. First, the improvement of the twin prime number theorem sieving method and the simplification of the calculation of the upper bound M. The second one is to introduce to you a conclusion that I summarized while studying the Polignac conjecture. New tool." Xu Qingzhou stood on the stage, briefly greeted everyone in the audience, and then got into the topic.
He first talked about the twin prime number theorem. "If P(z) represents the product of all prime numbers whose size does not exceed z, then the previous sieve method can be written as: S=∑N "When: gi(d)=μhi(d)=μ2(d)∏p|dgi(p)1gi(p) the 67th can be converted into: S=[1+o(1)]NlogN(kM2.O( R2log3kR)+O(E)” The first half of the content is not new, it just supplements the previous proof process. After talking for 20 minutes, Xu Qingzhou entered the second part. "As I said at the beginning, when studying Polignac's conjecture, I created a new tool-the harmonic sieve method." There was a commotion in the audience. "The blending sieving method? Is it an improved version of a certain classic sieving method?" "It should be." Everyone started talking quietly. The sieve method is one of the most effective tools for finding prime numbers or solving problems related to prime numbers. Common sieve methods are the sieve of Eratosthenes, the interval sieve method, etc., or improved versions of these sieve methods. Gu Zhizhong nodded slightly, his eyes curious, wanting to know what kind of screening method this kid had done. "In order to better study the distribution of prime numbers, I used the Selberg sieve method as a basis, in which I used solution sets and sequences to explore the properties of twin prime numbers." Xu Qingzhou went straight to the point and called out all the formulas.
The sound of flipping through notebooks rang out in the lecture hall. Ahead, Xu Qingzhou has already started: “Using (4), we get: 1(ΛΛ+Λ′)=1″, and do Möbius inversion on both sides, we get: ΛΛ+Λ′=μ1″.” "Finish the definition of Dirichlet convolution and the definition of derivative: ∑rd=nΛ(r)Λ(d)+Λ(n)lum_{rd=n}\mu(r)\log^2dag5” The narration part of the report is over. Many people in the audience were amazed and said that this screening method was perfect. It’s time for questions. Clearly, there is considerable interest in the blending sieve method. For example, a middle-aged professor got up and asked: "On page 53 of PPT, the necessary and sufficient condition for d to be solved is that q and k are mutually prime. We only need to consider the case where q and k are mutually prime. Here, what is Got it?” Xu Qingzhou thought for a moment and then said: "It is obtained through the sum of parts method. We only need to deal with the content on the right side of the equation: ∑qd≤xqd≡h(k)μ(q)log2d=∑q≤x(q,k)=1μ(q)∑d≤xd≡q1h(k)log2d” I also asked how to integrate the harmonic sequence into the sieve method. Xu Qingzhou answered one by one. The sixth questioner, the microphone was in the hands of an old acquaintance.
Gu Zhizhong's old enemy Pang Handong. Pang Handong did not raise the issue of the sieving method, but asked with a smile: "Classmate Xu Qingzhou, is this blending sieving method your entire achievement in the past six months?" "It's part of it." Xu Qingzhou replied calmly, understanding that the old man was looking for trouble. "Part of it?" Pang Handong smiled and continued: "Half a year ago, you took the Polignac conjecture as a project. Currently, many research institutions around the world are receiving good news. It seems that you haven't heard much news here. We are all very anxious." Xu Qingzhou said with a calm expression: "One of my teachers once said that you need to be attentive to study. I think it is right, and I have always used this as my code of conduct." Pang Handong's expression froze. Who didn't know that the old man Gu Zhizhong once ridiculed him for not concentrating on learning and doing miscellaneous things. Professor Gu also smiled slightly, thinking that this boy really has his own style. Pang Handong suppressed his anger and said with a smile: "Number theory, you young people still have ideas and it is not convenient to reveal your progress. After all, many scholars like me are looking forward to hearing your good news." As far as he knows, since this person applied for the project, he has participated in two major projects of the Komon Institute. No matter how unfavorable one person is, it is impossible for him to have the energy to study other projects. Didn't you Gu Zhizhong say that you should be steady in learning? How come your own students are hammering here and there? Although it wouldn't go too far, it was still simple to drag Xu Qingzhou over the fire. I just want you to tell me that the proof of Polignac's conjecture is not going well. (End of chapter)