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 Kathleen again.
This report was even hotter than the one in the morning. He was already 30 minutes ahead of schedule, but he still almost didn't even get a seat.
"There are too many people." Xu Qingzhou sighed.
Kathleen sat next to Xu Qingzhou, smiled and nodded, "This is Professor Maynard's lecture."
Professor Maynard, currently teaching at Oxford University, is a leader in the field of prime numbers. The theme of this report is also about the Riemann Hypothesis.
"What do you think the Riemann Hypothesis is?" Kathleen asked.
Xu Qingzhou thought for a while and said: "The Riemann Hypothesis, for us, may be similar to Fermat's last theorem before algebraic geometry came out."
Or a drawing of the Eiffel Tower from the Stone Age.
"Very accurate." Kathleen's eyes lit up, and she agreed very much with Xu Qingzhou's words.
Next door, the chat topic between two people has transitioned from the Riemann Hypothesis to the Twin Prime Conjecture. One of them has even laid out a few pieces of manuscript paper and is sketching on it.
Soon, a circle of people gathered around them, including Xu Qingzhou and Kathleen.
The main output of the conclusion was an Indian guy. He used an improved weighted sieve method, which was similar to Zhang Yitang's method. Both of them 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 twin prime pairs less than or equal to $x$. That is, if there is a prime number $p$ such that $p$ and $p+2$ are both prime numbers, then twin The prime number conjecture is equivalent to $\lim_{{xo\infty}}\pi_2(x)=\infty$.”
Kathleen stared at the manuscript paper tightly and thought seriously.
The people around him were also deep in thought, wondering what they could do next if they followed the Indian guy's thinking.
Compared with the Riemann Hypothesis, the twin prime conjecture seems not so unattainable.
Unlike everyone else, Xu Qingzhou was a little disappointed. This method was too bad. If it continued like this, let alone Zhang Yitang's prime number method, it would be a dead end.
"Believe me, as long as we continue to extrapolate, there is an 80% probability that we can prove the twin prime conjecture!"
Looking at the other party's vow, Xu Qingzhou couldn't help but said: "Now, the remaining m, for S-S/2-S/2-S, must satisfy r-2≤Ω(m)≤r, but obviously, If you continue to calculate, a result that is exclusive to this condition will appear.”
The Indian guy shook his head: "No, this will never happen. We are the first to find the lower bound of S."
"But your m has been calculated twice by (i) in S, and the lower bound you calculated 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 Yagir, also approves of this method."
Professor Yagier is well-known in the number theory circle. When he heard this name, the doubtful eyes around him suddenly disappeared.
But everyone who comes here has something, so they are not too excited and want to play it safe.
After all, it’s common for famous scholars to announce that they’ve proven a conjecture, only to have it disproven the next day.
However, there will also be people who 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?"
"Very welcome." The Indian guy smiled and looked at Xu Qingzhou provocatively.
Xu Qingzhou shrugged, returned to his seat, and did not continue the meaningless argument. He thought to himself that if it were so simple, he would have already solved it 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 convinced.
Kathleen chuckled: "I don't think so either."
At this time, the seats in the lecture hall were full, and there were even people standing in the aisles.
There is no way, Professor Maynard is considered one of the top mathematicians in the world, and the content of the lecture is the Riemann Hypothesis, which is currently very popular. Soon, a middle-aged man in a suit walked into the lecture hall.
Professor Maynard also went straight to the topic. At this time, the big screen displayed content that had been prepared long ago.
Report content: Estimation of new large values of Dirichlet polynomials.
In the audience, Xu Qingzhou opened his notebook and began to listen carefully.
"During this period we made the first substantial attempt to improve on the classical bounds on the zeros of the Riemannian zeta function established by Eingham around 1940"
"Of course, I have to mention Mr. Zhang Yitang's twin prime number conclusion here. By supplementing and improving this conclusion, we found that we can recalculate the new maximum value of the Dirichlet polynomial."
The argument is still based on Fourier analysis.
In Xu Qingzhou's view, the first few steps can be regarded as standard steps and are not difficult. Judging from the expressions of other people participating in the meeting, they should have the same idea as him.
Thirty minutes into the report meeting, a change finally occurred, or a clever choice.
For example, raising a key phase matrix to the sixth power can better describe and analyze the behavior of functions at different scales.
By the time they got here, the big guys sitting in front had already opened their notebooks and started making calculations based on Professor Maynard's ideas.
Solving a mathematical problem may be like building a bridge, building a little bit 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 certain exchanges in economy, transportation, culture, etc. between the two sides.
Significant.
1 hour passed.
Most of the question-and-answer period has passed.
Professor Maynard looked around the lecture hall and said, "Sorry, due to time constraints, I can only answer the last person's question."
Someone raised their hand.
There were quite a few people who wanted to ask questions, roughly four or five of them, including Xu Qingzhou who had been deep in thought and the Indian guy.
Professor Maynard's eyes fell on Xu Qingzhou. Compared with the others, this questioner was too young.
So, as a person who studies prime numbers, he immediately thought of the young man who had just proved Kramer's theorem.
Professor Maynard looked at Xu Qingzhou and said, "Sir, you can speak now."
He was looking forward to the young man asking novel questions.
Next to him, the Indian guy who wasn't picked on was a little bitter. It's this annoying guy again. Huh, he wants to see what he has to say.
Katherine looked at Xu Qingzhou curiously with her beautiful eyes.
Xu Qingzhou nodded and said: "Logically speaking, this kind of interval improvement research method requires some special skills to bring positive benefits to the conclusion."
"That's right."
Professor Maynard nodded slightly. The young man did not disappoint him. He found the problem at a glance. He also admitted: "Unfortunately, before this report meeting, we only calculated so far. The next step is very critical, but We don’t have any specific ideas at the moment.”
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 looked serious and made a gesture of invitation.
Xu Qingzhou calmly stood up and walked towards the podium, while the staff on the side had already pushed up a clean blackboard.
On the podium, he picked up the chalk and wrote a series of complex formulas on the blackboard.
∑∞left(\frac\Gamma\left(\frac{s+\delta}{2}\right)
(End of this chapter)