Chapter 197 Cycle
Wu Tong always keeps his word. When he said he would return to mathematics, he took action immediately. The Goldbach conjecture has been delayed for too long. The research is too fragmentary. It is better to devote yourself to it wholeheartedly.
She began to go regularly between the Mathematical Research Center, the library, and the dormitory, devoting herself to the research on the Goldbach conjecture. She read the manuscripts of her predecessors over and over again. She tried the sieve method, the circle method, and various methods that had been used to solve the Goldbach conjecture. She needed a tool to solve the Goldbach conjecture.
It is said that the screening method has reached its end. After trying it herself, Wu Tong did not agree with this view. She finally confirmed that she still needed to make progress in the screening method and lay a solid foundation for climbing to the top of the Kochi.
Wu Tong wants to finish researching the information related to Ge Chai as soon as possible. If all goes well, he can finish the project in March. After that, he may have time to go home for a while. Then he can wait for one to two months for the graduation defense and prepare for graduation.
Thinking about being able to stay at home for one or two months, Wu Tong became more motivated. Every question has an answer. Wu Tong was happy and immersed in her research. The difficulties that bothered the world and made people hesitate to move forward were just a step that was a little harder for her to climb, not an insurmountable step.
Wu Tong finally chose to introduce the sieve method into the circle method to supplement and innovate the sieve method.
When studying many number theory problems, we often use generating functions. For example, when studying the distribution of prime numbers, we use the Dirichlet series... By applying the Perron formula, the analytical properties of F(s) can be used to study many multiplicative number theory problems...
By making more clever use of the circle method, predecessors have proved that almost all even numbers satisfy the strong Goldbach conjecture...
The sieve method is actually a broader idea. Using this method, some number theory quantities can be estimated. For the simplest example, if π(x, z) represents the number of positive integers whose size does not exceed x but all prime factors are greater than z:
π(x, z) is a typical sieve function. Sieve method is a method used to estimate this type of function. Sieve method plays an important role in Goldbach problem. To be more precise, this form of sieve method is used in the study of {a, b} problem...
Wu Tong thought about the sieve method and the circle method, and deduced bit by bit how to combine them skillfully to create a ladder to overcome Ge's guess.
The number of solutions of N=p1+p2+p3 (prime numbers p1, p2, p3 are all ≥ 3)...
The problem of A+B is, after all, a complex expression of Goldbach's idea. Every large even number N can be expressed as a+b. The number of prime factors of AB does not exceed A and B respectively. When A=B=1, the problem naturally returns to the original expression. Any even number greater than 2 can be written as the sum of two prime numbers.
In the form of 1+1, the way forward still lies in the Goldbach conjecture itself, the number of prime factors is 1.
When looking for the best way to combine the sieve method and the circle method, Wu Tong thought again of the time at the beginning of last year when she was reminded by Lu Xiao in the library that the topological sieve method was originally an extension of Professor Zellberg's attempts to charge at the Goldbach conjecture. She remembered her own infinite group proof method...
Thoughts collide here, sparks splash out a new chapter. Wu Tong looked out the window. At this time, the spring breeze was blowing, the earth was warming up, and the ground was dyed green. Spring, summer, autumn and winter, the four seasons are a cycle. The charge of Goldbach's conjecture, is it not also a cycle?
The extreme of sieve method...the closed orbit integral and residue theorem of circle method, the infinite topology of group theory...all are intertwined in Wu Tong's mind and merged into a splendid chapter.
Wu Tong's eyes were fixed on the budding forsythia flowers outside the window. She thought that she had found the way to climb Mount Everest. Once the road was completed, reaching the summit would be a natural thing.
Wu Tong had done a lot of bridge and road construction before, so he was now very familiar with it. His writing was smooth, and the steps of climbing the mountain were condensed at the tip of Wu Tong's pen.
Although she has not made any new research in mathematics in the past six months, all her research is based on mathematics. With sufficient training, Wu Tong has made great progress in mastering and consolidating mathematics.
Now, when he really started to do mathematical research, it was like the wind adding fuel to the fire. It spread all over the prairie in an instant. The progress was smoother than Wu Tong had expected. It was the result of the accumulation of small trickles.
Wu Tong was not as inspired as she used to be, working all night. She was now in a special state every day, still following the routine of going to work, but Cai Yi and others who followed Wu Tong could see that Wu Tong's state was not right at the moment, she was more like immersed in her own world.
Cai Yi and the other two, who had seen enough of Wu Tong's special condition, responded quickly and arranged for An Wenshu to be Wu Tong's assistant, to follow her and help her avoid possible disturbances on the road. The research center contacted Professor Zhou and avoided the disturbances to Wu Tong from the research center.
Wu Tong has been immersed in this special state, resting, eating, doing research, and repeating for a week. Thick manuscripts of deductions piled up on Wu Tong's desk. By chance, she wrote the last stroke of the proof method she named the sieve circle method, conquering the mathematical mountain of Ge Guess, and the dawn of the crown jewel of number theory has been lit.
"Professor Zhou, starting tomorrow I will be in seclusion, focusing on solving the Goldbach conjecture. I will not come to the Mathematical Research Center for the time being!" Later, Wu Tong knocked on the door of Professor Zhou's office opposite the laboratory, entered the office and reported to him.
Zhou Wenping was marking students' papers, and his horizons were raised by Wu Tong's achievements. Every time he saw a student paper, he had to keep himself calm. There was only one Wu Tong, and not everyone was a super student like Wu Tong.
Just as he was thinking that Wu Tong was in a special research state recently, and who knows when, he would give them a world-shaking achievement, he saw Wu Tong pushing the door in. He couldn't help but look surprised, "Wu Tong, you have already..."
Did you figure out Ge Guess? He didn't dare to ask this question. Wu Tong had only been back for less than ten days. If he had already figured out Ge Guess, he felt that he needed a quick-acting heart-saving pill!
"Not so fast, Professor Zhou!" Wu Tong's words made Zhou Wenping's heart settle down a little. He said, I guess it's so easy to do, it won't take hundreds of years for anyone to make great results.
But then Wu Tong said, "I have found a way and worked out a method to overcome the conjecture. What remains is to retreat and substitute the conjecture into the proof. Professor Zhou, please wait for another week or two and wait for my surprise!"
"Ah..." What a big surprise. You can figure it out within a week or two?
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