Chapter 180 I May Need to Borrow the Blackboard After a 30-minute break at noon, Xu Qingzhou came to the lecture hall again at 2 o'clock. To his surprise, he met Catherine again. This report was even more popular than the one in the morning. He had arrived 30 minutes early, but still almost failed to get a seat. "There are too many people." Xu Qingzhou sighed. Kathryn was sitting next to Xu Qingzhou. She smiled and nodded, "This is Professor Maynard's lecture." Professor Maynard, who currently teaches at Oxford University, is a leading figure in the field of prime numbers, and the theme of this report is also about the Riemann hypothesis. "What do you think the Riemann hypothesis is?" asked Catherine. Xu Qingzhou thought for a moment and said, "The Riemann hypothesis may be similar to Fermat's Last Theorem before algebraic geometry was invented for us." Or maybe a Stone Age blueprint of the Eiffel Tower. "Very accurate." Catherine's eyes lit up and she agreed very much with what Xu Qingzhou said.
Next door, the topic of conversation between two people has shifted from the Riemann hypothesis to the twin prime conjecture, and one of them has even spread out a few sheets of manuscript paper and is drawing on them. Soon, a circle of people gathered around, including Xu Qingzhou and Catherine. The main output of the conclusion was made by an Indian guy. He used an improved weighted sieving method, which is similar to Zhang Yitang's method, and both methods made adjustments to the distribution of arithmetic series. The Indian guy said in curry-flavored English: "Here, we define $\pi_2(x)$ as the number of pairs of twin primes less than or equal to $ x $. That is, if there exists a prime number $ p $ such that $ p $ and $ p+2 $ are both prime, then the twin prime conjecture is equivalent to $\lim_{{xo \infty}}\pi_2(x)=\infty $." Catherine stared at the manuscript, thinking seriously. The people around him also fell into deep thought, wondering how to deduce the next step if they followed the Indian guy's thinking. Compared with the Riemann hypothesis, the twin prime conjecture does not seem so out of reach. Unlike everyone else, Xu Qingzhou was a little disappointed. This method was too bad. If he continued like this, it would be a dead end, not to mention being on par with Zhang Yitang's prime number method. "Believe me, as long as we continue to calculate, there is an 80% chance that we can prove the twin prime conjecture!" Seeing the other party's confident look, Xu Qingzhou couldn't help but say, "Now, the remaining m, for S-S/2-S/2-S, must satisfy r-2≤Ω(m)≤r. But obviously, if we continue to calculate, a result that contradicts this condition will appear." The Indian guy shook his head: "No, this will never happen. We have already found the lower bound of S." "But your m has been calculated twice by (i) in S, so the lower bound you found is inaccurate." Xu Qingzhou smiled. The Indian guy was silent for a moment, but still insisted on his point of view, "No, I think there is nothing wrong with our calculations. As long as we extend it, there will definitely be results." As if to verify his conclusion, he added: "My teacher, Professor Yajil, also approves of this method." Professor Yajil is well-known in the number theory circle, and when people heard his name, the questioning looks around him suddenly decreased. But everyone who came here had something, so they were not too excited and planned to play it safe. After all, it is common for a famous scholar to announce that he has proved a conjecture, only to have it overturned the next day. However, some people are interested. For example, a young man took out his business card and said, "Sir, I am from Loughborough University. Are you interested in studying this topic together?"
"You are very welcome." The Indian guy smiled and looked at Xu Qingzhou provocatively. Xu Qingzhou shrugged and returned to his seat without continuing the meaningless argument. He thought that if it was that simple, he would have already figured it out during the Chinese New Year. Kathleen asked Xu Qingzhou: "Do you think he can succeed?" "No." This time it was Xu Qingzhou's turn to be sure. Kathryn chuckled. "I don't think so either." At this time, the seats in the lecture hall were full, and people were even standing in the aisles. There was no other way. Professor Maynard was one of the world's top mathematicians, and the content of the lecture was the currently very popular Riemann hypothesis. Soon, a middle-aged man in a suit walked into the lecture hall. Professor Maynard also went straight to the point. At this time, the big screen was showing the content that had been prepared long ago. Report content: New large value estimates of Dirichlet polynomials. Below the stage, Xu Qingzhou opened his notebook and began to listen attentively. "During this period, we made the first attempts to make substantial improvements on the classical bounds on the zeros of the Riemann zeta function that Ingham had given around 1940." "Of course, we have to mention Mr. Zhang Yitang's twin prime conclusion here. By supplementing and improving this conclusion, we found that we can recalculate the new large value of the Dirichlet polynomial." The argument is still based on Fourier analysis. In Xu Qingzhou's opinion, the first few steps can be regarded as standard steps and are not difficult. Judging from the expressions of other participants, they should have the same idea as him. Thirty minutes into the lecture, a change finally occurred, or a clever choice. For example, by raising a key phase matrix to the sixth power, we can better describe and analyze the behavior of functions at different scales. By this time, the big guys sitting in the front had already opened their notebooks and started to calculate based on Professor Maynard's ideas. Solving a math problem may be like building a bridge. You add a little on the left and a little on the right, but there is a section missing in the middle. Professor Maynard's achievement is equivalent to extending the bridge. Although it has not been completely repaired, it has enabled a certain degree of exchange in terms of economy, transportation, culture, etc. between the two sides. Significant. 1 hours passed. Most of the question-and-answer session has passed. Professor Maynard looked around the lecture hall and said, "I'm sorry, due to time constraints, I can only answer the last question." Someone raised their hand. There were quite a few people who wanted to ask questions, about four or five, including Xu Qingzhou who had been in deep thought and the Indian guy. Professor Maynard's eyes fell on Xu Qingzhou. Compared with the others, this questioner was too young. So much so that, as a person who studies prime numbers, the first person he thought of was the young man who had just proved Cramer's theorem. Professor Maynard looked at Xu Qingzhou and said, "Sir, you may speak now."
He was looking forward to the young man asking some novel questions. Next to him, the Indian guy who was not called was a little jealous. It was this annoying guy again. Humph, he wanted to see what insights he could come up with. Catherine looked at Xu Qingzhou curiously with her beautiful eyes. Xu Qingzhou nodded and said, "Logically speaking, this interval improvement research method requires some special techniques to bring positive benefits to the conclusion." "Yes." Professor Maynard nodded slightly. This young man did not disappoint him. He found the problem at a glance. He also admitted: "Unfortunately, before this report meeting, we have only deduced so far. The next step is crucial, but we currently have no specific ideas." Xu Qingzhou nodded and glanced at his notebook. "I have some ideas. If possible, I need to borrow the blackboard." "Please feel free to use it." Professor Maynard said seriously and made a gesture of invitation. Xu Qingzhou stood up calmly and walked towards the podium, while the staff on the side had already pushed up a clean blackboard. At the podium, he picked up a piece of chalk and wrote a series of complicated formulas on the blackboard. ∑∞left(\frac\Gamma\left(\frac{s+\delta}{2}\right) (End of this chapter)