Chapter 399: Three world-class mathematical conjectures, can you still beat me in seconds? Xu Qingzhou's life was very fulfilling. He would attend lectures, look up materials in the library, or go home to do calculations. Apart from the fact that the academic atmosphere became stronger and the people around him were basically foreigners, his life seemed to have not changed much. Still in free-range mode. During this period, a major event happened in the mathematics community. Young mathematician Jerry Brunson proved the Strong-Mersene conjecture. After reading the other party’s introduction, Xu Qingzhou exclaimed, “Wow!” He introduced Hochian theory into combinatorics, proved the Dowling–Wilson conjecture for geometric lattices, proved the Heron–Rota–Welsh conjecture for pseudo-matrices, and developed the Lorentz polynomials. There are at most four Fields Medals in total, so the academic community has begun predicting the winner of the 18 Fields Medal. The most popular candidate is of course Xu Qingzhou himself. Cramer's conjecture, twin prime conjecture, Polignac's conjecture. The second is the young mathematician Jonathan Birmingham, who proved the exponential ergodicity of solutions under 1-Wasserstein distance and proposed a criterion for the exponential ergodicity of Markov semigroups on Banach space under 1-Wasserstein distance.
The third one is Jerry Bronson. Xu Qingzhou didn't feel much pressure. I have three world-class mathematical conjectures in my hand, can you beat me in one second? Except for the fact that someone solved two Millennium Problems directly within this year and crushed them all, otherwise, the Fields Medal would definitely be a winner. On July 26, Professor Roberts returned from a seminar in New York, and Xu Qingzhou was also preparing to go to the office. Passing by the big dome that is the symbol of MIT, you can see students sitting outside the Stratton Student Center and basking in the sun. There are also nearby residents camping on the lawn along the way. Compared to this, there is not much sense of urgency that I feel when walking on the road to Beijing University. Just talking about the academic atmosphere, one can clearly feel the gap between China and abroad. MIT is not big. Compared with some of the 985 universities in China, it can even be said to be a bit miniature. But such a school attracts a large number of students. "The future of China will get better and better." Xu Qingzhou is very confident. He sighed inwardly again, as expected, the status of Mizuki Kyoda in the hearts of the Xia people is the same as the status of A shares in the hearts of stock investors. Xu Qingzhou had just arrived downstairs at the Mathematics Department when he suddenly saw a familiar figure, who was waiting for him with a smile. He looked at the handsome man in a suit in front of him and was stunned for a moment. "Are you Horn?" "Hi, Xu, nice to see you again." Horn waved. Xu Qingzhou was greatly surprised, if it wasn't for the similar body shape, he would never have recognized him. Now after cleaning up a little, you know what a fat version of Thor is. No wonder this guy said women are passionate Although he was surprised, he still corrected himself: "It's Xu, not Xu." "The Chinese language in your Xia country is really too difficult." Horn sighed, paused, and said, "Ok, Xu, when this is over, do you want to go for a drink? A friend of mine happened to introduce you to your fan." Xu Qingzhou gave up explaining that he was not weak.
He said helplessly: "I'm sorry, I have other plans tonight, I'm afraid I don't have time to drink with you." Horn shrugged regretfully and didn't force it. As they walked, he asked, "Is your Riemann hypothesis going well?" "I have some general research directions." Xu Qingzhou sighed and said that the Riemann hypothesis was indeed one of the seven problems of the millennium. It was more difficult than any other problem he had encountered before and was very tricky. It could be said that it was difficult at the beginning, difficult in the middle, and there was no end in sight at the end. Professor Roberts is good at studying number theoretic functions, and he just happens to have several function problems on integer sets. "That's amazing! I tried it before, but gave up after just one week." Horn was amazed. The Riemann hypothesis is like a hidden treasure in the kingdom of mathematics. Countless wise men have spent their entire lives searching for it, but its mystery has not yet been uncovered. The most important thing is that this treasure is laid naked in front of everyone, telling you: It is here, as long as you can find the way. Horn glanced at the young face beside him. Although this Xu Qingzhou has created several miracles, it is difficult for him to win if his opponent is the Riemann hypothesis. Professor Roberts was looking through a stack of manuscripts. When he saw Xu Qingzhou come in, he asked Xu Qingzhou to sit down and stuffed the manuscripts onto a bookshelf on the side. The office is still the same as before, giving people a mysterious feeling in its clutter. Xu Qingzhou greeted him and told him his current thoughts. "Inequality? The Landau-Siegel zero point conjecture is a good idea." Professor Roberts thought for a moment and nodded slightly. Xu Qingzhou continued: "Then we use the inequality to construct a mathematical structure related to the existence of the Landau-Siegel zero. Next, we use the introduced inequality and mathematical model to make inferences." As for why Xu Qingzhou suddenly thought of the Landau-Siegel zero, we need to talk about the Dirichlet L function first. Professor Maynard and his team proved new bounds on the frequency with which the Dirichlet polynomials take on large values. The reason why this thing is important is that if the Dirichlet characteristic χ(n) is taken as a trivial characteristic that is always equal to 1, then the Dirichlet L function becomes the Riemann zeta function. Furthermore, the generalized Riemann hypothesis is a generalization of the Riemann hypothesis, which states that the real part of all non-trivial zeros of the Dirichlet L function is equal to 1/2. Going one step further, there are the Landau-Siegel zeros that are related to the Dirichlet L function. Xu Qingzhou’s idea was very simple, to solve the Landau-Siegel zero point problem first. The Riemann hypothesis is a conjecture about the distribution of zeros of the Riemann zeta function, and the Landau-Siegel zero problem is a special case of the generalized Riemann hypothesis, or a special zero point related to it. This zero point is speculated to exist at some special position of the Dirichlet L function. If the Landau-Siegel zero exists, then the Riemann hypothesis is wrong. Conversely, if the Landau-Siegel zero does not exist, then there is no conflict with the Riemann hypothesis. Both Professor Roberts and Horn expressed their approval of Xu Qingzhou's idea, but they were not overly surprised because no matter how you look at it, it is still like looking for a needle in a haystack. Over the past century, many mathematicians have proposed corresponding solutions, but in reality Xu Qingzhou didn't care. At least he had a specific range. At worst he would just find a way to fish it out from the bottom of the sea. After explaining his plan, he also took out the manuscript and asked Professor Roberts for advice on several difficult problems he had encountered during this period. After Xu Qingzhou came out from Professor Roberts' place, around 6: in the afternoon, he took a taxi and went to a ring store called "Cartier" in downtown Boston. School Beauty Song’s birthday is on the 5th of next month, so he has to bring the gift back in advance. This is a pair of white couple rings that he had ordered ten days ago, engraved with Xu Qingzhou and Song Yao’s names.
(End of this chapter)