Chapter 319 I have a student, not bad Ding ~ Ding ~ There were several more photos in the group. The protagonists in all the photos were in the same posture, with their hands clasped together and solemn expressions, as if they were performing some mysterious ritual. Xu Zhengyang: "Old Xu, your seat has become a check-in spot." Xu Qingzhou: “???” Zhai Ziqiang: "It's the final exam, let's all come and take advantage of your glory." Looking at the group chat where Xu Zhengyang posted another photo of a boy sitting in his seat to "pay tribute", Xu Qingzhou was silent for a long time and replied: "Awesome." If you think about it carefully, you can actually understand it a little bit. The math exams at Kyoto University are notoriously horrible, otherwise there wouldn't be so many people entering the school with high hopes, only to be hit hard in the first semester and start to doubt their lives. Despair eventually turns into metaphysics. Xu Zhengyang: "Let's discuss charging admission, or simply set up a Xushen Sect, and you will be the spiritual totem."
Xu Qingzhou: "Remember to split the ticket fee with me 50-50." After chatting with a few Moriguchi in the group for a few minutes, Xu Qingzhou put down his phone. He saw Song Yao sent a message saying that he was going to read a book. He didn't waste time and turned to the part he had read yesterday at noon. He soon immersed himself in the complicated formulas. At the same time, Meng Bin went to the office to get Gu Zhizhong's teacup. He wanted to fill the cup with water for Gu Zhizhong so that he could drink it directly when Gu Zhizhong came. After getting the water, he went to the Q&A room. There are quite a lot of people in the Q&A room. During exam week, the test takers are even crazier than before. Everyone holds their breath and makes the final sprint. Meng Bin had just put Gu Zhizhong's teacup away when a student came up with a question. "Brother Meng, can you explain this question to me?" Meng Bin took a look and saw that it was a question that extended multivariate calculus to multidimensional space. It was not difficult for him, so he picked up the manuscript paper and did a few calculations. After a moment, he said: "Here, since the integration area D is the unit circle, the calculation can be simplified by using polar coordinate transformation. Therefore, we can convert the original double integral into polar coordinate form for calculation." The boy nodded, said thank you, and went downstairs to do the calculation. This is normal. Since Professor Gu was not here, he and senior brother Su Kewei helped to answer the questions. Of course, even though they are graduate students, they can’t solve all the problems. Mathematics seems to be the same, but the research direction is different and the content is very different, not to mention that the top scorers of Kyoto University are not ordinary. Some undergraduate students were working on topics that were even more complicated than those of his master’s students when he was at Shu University. For example, the homology group of topological space in algebraic topology is used to distinguish different topological structures, and the modeling and analysis methods of nonlinear dynamic systems. look. These undergraduate students’ topics are more challenging than each other. At this time, a message came from Meng Bin's mobile phone. Gu Zhizhong has to meet a friend and will come later. He remembered that Professor Chen Lixin, who had returned from the United States, seemed to be a classmate of his teacher Gu Zhizhong. They had gone to Princeton to study together, and after graduation, Chen Lixin stayed there to teach. "Senior brother." A girl handed over a question.
【Riemann zeta function and prime number theorem】 Looking at the questions, Meng Bin started to have a headache. The girl said: "I tried to prove the prime number theorem by applying complex analysis. In order to connect the prime number theorem with complex analysis, I have extended the Riemann zeta function from the real number field to the complex number field. However, in the Dirichlet series, there is no way to make s∈C satisfy σ>σ0 and f(s) absolutely converge." Meng Bin was in a dilemma. He was not a prime number researcher, so it seemed that he had no choice but to wait for Professor Gu to come. Ever since Junior Brother Xu solved the three prime number conjectures, there has been a wave of prime number research in the School of Mathematics. etc. Meng Bin paused and suddenly thought, why wait for Professor Gu, isn’t Junior Brother Xu here? He glanced at the boy next to the girl, "Do you both have problems with prime numbers?" "Ah." Meng Bin stood up and said, "Wait a moment, I'll find a teacher for you." "teacher?" “Definitely a master in prime numbers.” Meng Bin smiled gently, stood up and walked out of the classroom. A few minutes later, everyone saw two figures walking in, one of them was Meng Bin, and the other looked familiar. Xu Qingzhou felt helpless. Everything was going well, but then Meng Bin rushed into the classroom and said he needed his help. "Xu Shen!" Someone recognized Xu Qingzhou, and everyone looked up. For a moment, there was a little commotion in the classroom. Meng Bin said with a smile: "Don't get excited, if you have any questions, just ask one by one." It was normal for these students to be excited. In their eyes, Xu Qingzhou was the kind of super boss who had broken through the void and ascended to the upper realm long ago. Not to mention the undergraduates, if they had not known Junior Brother Xu before, they would probably have the urge to worship the boss when they first saw him. "Junior brother, I'll leave it to you then." "Okay." Xu Qingzhou nodded and sat down at the table in the front row. Since Professor Gu wanted to meet an old friend, it was only right for him to help out. The girl who first asked the prime number question blushed and handed over the manuscript. Xu Qingzhou took a look and thought it was not difficult. He said directly: "For this part, since the series converges, the partial sum is bounded. You can try to apply the estimation formula in above the lemma and use the Cauchy convergence principle to prove it." “Cauchy Convergence Principle?” "Next, you must want to extend ζ(s) to a meromorphic function on the right half plane." "Yeah, yeah! Yes! God Xu, you are so awesome!" Xu Qingzhou shook his head modestly and said, "No problem, but you have to pay attention to the need to use the open cover principle to establish a series of ordered points on γ for the finite open cover." Professor's office. The old man wearing gold-rimmed glasses looked around Gu Zhizhong's office and said with a smile, "Old Gu, the office is nice." "good." Gu Zhizhong calmly poured tea for Chen Lixin, "You old man, you haven't been back for more than ten years, why did you suddenly think of returning to China and come to see me?" He and Chen Lixin were rivals, having competed from Peking University to Princeton, but they were also friends who respected each other.
"I just want to go back to my hometown. I'm getting old and I'm beginning to miss home. Old Gu, actually, with your personality, you're more suitable for teaching outside." Gu Zhizhong is stubborn and sticks to his own opinions, which puts him at a disadvantage in China, where human relationships are mixed and social conventions are mixed. Moreover, the assessment system of domestic universities places too much emphasis on short-term results, and everyone is busy completing those scientific research targets. "Everyone has their own way of living. There are only foreigners abroad, and I can't get used to it." Gu Zhizhong waved his hand and said with a smile: "How have you been these years?" "Not bad. I became a tenured professor at Princeton a few years ago. Now I have the time to devote all my energy to scientific research." Chen Lixin took a sip of tea. Gu Zhizhong narrowed his eyes and knew that this old guy would not come to see him specifically. Judging from his attitude, he was obviously here to show off. If it were in the past, Gu Zhizhong would probably have cursed inwardly, but now, hehe, he probably doesn’t know that I have a student named “Xu Qingzhou”. Chen Lixin really didn't know that Xu Qingzhou was Gu Zhizhong's student. The few papers he had seen were all signed by Xu Qingzhou himself, without even the title of corresponding author. The two began to talk about what had happened over the years. Chen Lixin really came here to show off. In the past, he was always inferior to that old guy Gu Zhizhong. But now, his career is going smoothly and he has many disciples. Gu Zhizhong is even a professor. However, Gu Zhizhong is very good at health preservation. After he said so much, Gu Zhizhong just smiled and agreed without frowning at all. After 20 minutes. Seeing that the time was almost up, Gu Zhizhong said, "You can have some tea first, or walk around the school. I'm on duty today, so I need to sit in the Q&A room for a few minutes." Chen Lixin stopped drinking tea and said with a smile, "Come together. It's a good opportunity to see what your students look like." "it is good." As the two walked out of the office, Chen Lixin said with emotion: "Xu Qingzhou from your School of Mathematics, well, this young man is very good, a rare mathematical genius." "Xu Qingzhou? He's okay." Gu Zhizhong said calmly. "Not bad? I'm praising Xu Qingzhou, why are you being so modest? You're still as modest as ever. Speaking of students, I just accepted a student this year, and he's very talented." Chen Lixin began to talk about his students. Just as parents start comparing their children when they reach a certain age, old professors start comparing their students when they reach a certain stage. "Then you are lucky." Gu Zhizhong said lightly. Chen Lixin had a smug look on his face: "Not bad, this kid won the gold medal in MCM (two American Collegiate Mathematical Contest in Modeling), he is much better than us back then." "It's awesome." Gu Zhizhong continued to compliment. As they approached the question-and-answer room, they could faintly hear the sound of someone giving a lecture, and they both stopped. "Here, we already know that ζ(s) has a meromorphic extension to Re(s)=0, and s=1 is its only extreme point. Therefore, there exists an analytic function g(s) on Re(s)>0, g(1)≠0" Listening to the people inside talking, Gu Zhizhong was slightly startled, and then he smiled meaningfully. Chen Lixin listened for a while and asked suspiciously, "Is this person talking about remedying the problem of Stein's proposition and proof of estimating the upper bound of ζ(s)?"
Gu Zhizhong nodded slightly. “The logic is clear, the process is simple, and it seems to be very insightful in the field of prime numbers.” After Chen Lixin finished his evaluation, he paused and asked in confusion: "You sound very young, are you a student?" "Well, a student I taught before, probably saw that I was not around, so he came to help." "You have a good student." Chen Lixin nodded. Although they had never met, he could feel from the other person's words that this person had already reached the level of his own student. "Barely okay." As they talked, the two of them walked into the Q&A room. (End of this chapter)