Wu Tong always kept his word. When he announced his return to mathematics, he immediately took action. He had been putting off studying the Goldbach conjecture for far too long. Sporadic research was too fragmented; it was better to devote himself wholeheartedly.
She began to regularly go between the Mathematical Research Center, the library, and the dormitory, devoting herself to the research on the Goldbach conjecture. She repeatedly read the manuscripts of her predecessors, and tried the sieve method, the circle method, and various methods that people had used to try to solve the Goldbach conjecture. Wu Tong had tried them all. She needed a tool to solve the Goldbach conjecture.
Some say the sieving method has reached its limit. After personally experimenting with it, Wu Tong disagrees. She ultimately confirms that further progress is needed to lay the foundation for a solid climb to the top of the sieving method.
Wu Tong wants to finish researching the information related to Ge Cai 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, and then wait for one to two months for the graduation defense and prepare for graduation.
The thought of being able to stay home for a month or two fueled Wu Tong's enthusiasm. Every question had an answer. Digging deep into her research, Wu Tong found joy and immersion. The difficulties that plagued most people were merely steps to her, not insurmountable ones.
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, generating functions are often used. 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 applying the circle method more cleverly, our predecessors have proved that almost all even numbers satisfy the strong Goldbach conjecture...
The sieve method is actually a broader idea. Using this method, we can estimate some number theory quantities. For example, if we use π(x, z) to represent 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 methods are used to estimate this type of function. Sieve methods play an important role in the Goldbach problem. More specifically, this form of sieve method is used in the study of the {a, b} problem...
Wu Tong pondered over the sieve method and the circle method, deducing bit by bit how to combine them skillfully to create a ladder to conquer Ge's conjecture.
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.
While searching for the best way to combine the sieve method and the circle method, Wu Tong thought again of the time around the beginning of last year when Lu Xiao reminded her in the library that the topological sieve method was an extension of Professor Zellberg's attempts to attack the Goldbach conjecture. She remembered her own infinite group proof method...
Thoughts collided here, sparks splashed 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, and the charge of Goldbach's conjecture is also a cycle, isn't it?
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, forming a splendid chapter.
Wu Tong's eyes were fixed on the budding forsythia 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 pen wrote smoothly, and the steps of the mountain climbed together 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, truly engaging in mathematical research was like a gust of wind fanning a blaze. It spread rapidly. The progress was smoother than Wu Tong had anticipated, a natural progression of the accumulated success of small steps.
Wu Tong wasn't as inspired as she used to be, working through the night. Instead, she was in a strange state every day, still sticking to her routine. But Cai Yi and the others who followed her could tell something wasn't quite right; she was lost in her own world.
Cai Yi and the other two, already well-versed in Wu Tong's unusual condition, quickly arranged for An Wenshu to serve as her personal assistant, accompanying her and helping her avoid potential disturbances along the way. The research center contacted Professor Zhou, preventing anyone from disturbing Wu Tong.
Wu Tong remained immersed in this peculiar state, resting, eating, and researching, a cycle that lasted a week. Thick manuscripts piled up on Wu Tong's desk. As luck would have it, she put pen to paper on the final stroke of the proof she had named the sieve method. Conquering the mathematical chasm of the Ge conjecture, the dawn of the crown jewel of number theory had begun.
"Professor Zhou, starting tomorrow I will be in seclusion, focusing on solving the Goldbach conjecture, and will not come to the Mathematical Research Center for the time being!" Later, Wu Tong knocked on the door of Professor Zhou's office across the street, entered the office and reported to him.
Zhou Wenping was originally 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 about Wu Tong's recent special research state, and who knows when he will give them another 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 ask this question. Wu Tong had only been back for less than ten days. If he had already figured out Ge Guess, he felt he would need a quick-acting heart 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 not that easy to do. It won't take hundreds of years for anyone to make great achievements.
But then Wu Tong added, "I've already found a way and devised a method to overcome the Conjecture. All that's left is to retreat and substitute the Conjecture into the proof. Professor Zhou, please wait a 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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