Chapter 223: Landau-Siegel Zero Point Problem
"I plan to start with the Landau-Siegel zero point problem." Lu Shan expressed his plan.
"It's a good choice." Chen Qiyi nodded in affirmation.
The Landau-Siegel zero is defined as a counterexample to the generalized Riemann hypothesis, and the conjecture that such zeros do not exist is called the Landau-Siegel conjecture.
If the Landau-Siegel zero exists, the generalized Riemann hypothesis is wrong, so we need to prove that it does not exist.
Studying the Landau-Siegel theorem involves the problem of non-trivial zeros of the Dirichlet L function. It is found that when special properties are met, the corresponding L function will inevitably have zeros with abnormal positions.
This possible zero point is not located on the straight line of the real part 1/2, but very close to 1. This zero point is called the Landau-Siegel zero point.
In the Dirichlet L function, there is at most one such zero point, and the real part is close to 1.
What does this have to do with the Riemann hypothesis?
The premise for the Riemann hypothesis and the generalized Riemann hypothesis to hold is that all non-trivial zeros of the zeta function or the L function are located on the straight line whose real part is equal to in the complex plane.
So this is the contradiction relationship mentioned at the beginning.
Proving that the Landau-Siegel zero does not exist proves that the Riemann hypothesis exists, and then we can prove the generalized Riemann hypothesis, and finally prove the Riemann hypothesis.
The key point here lies in the Dirichlet L function, which is similar to the Riemann zeta function in many aspects and can correspond to each other.
For example, the zeros of the Dirichlet L function can be divided into trivial and non-trivial, and all non-trivial zeros are located in the band area (., the critical band) where 0＜Re(s)＜1.
Corresponding to the Riemann hypothesis of the Riemann zeta function, there is the generalized Riemann hypothesis of the Dirichlet L function.
When all Dirichlet characteristics are 1, they simplify to the Riemann zeta function.
The Riemann function is a special case of the Dirichlet L function and is also the simplest case.
Since the Dirichlet L function is a generalization of the Riemann zeta function, the generalized Riemann hypothesis is obviously a generalization of the Riemann hypothesis.
This is the entire logic of the proof.
An important concept here is the paper on twin prime pairs published by Lu Shan before. Dirichlet's theorem talks about the prime number problem in arithmetic series.
When mathematics reaches the highest level, even numbers can hardly be seen, only symbols. High-end mathematics is logic, deriving new theorems from existing theorems one by one. If it makes sense, it is right, and if it doesn’t make sense, it is wrong.
Therefore, the essence of mathematics is a tool, a generalization, which is basically the same thing as computer logic.
In his previous life, Tang Yi proved the Landau-Siegel zero point problem in 2022, but there is still controversy in the academic community. What Lu Shan has to do is to solve this problem completely.
Lu Shan talked a lot about his ideas, but Chen Qiyi didn't fully understand. Mathematics is like this, if you understand it, you understand it, and if you don't understand it, you don't understand it. It has nothing to do with status, but only with talent.
Chen Qiyi did not give any valuable inspiration, so Lu Shan still had to rely on the Singularity Laboratory to discuss with Poincare.
"Throughout, t, u, v, z and σ denote real variables; x and y denote positive real variables; s and w denote complex variables s = σ + it, w = u + iv; dhjklm, n and r denote natural numbers, p and q denote prime numbers; the arithmetic functions 3 (n) and (n) are defined as usual, and τk(n) denotes the k-fold divisor function. Let ∑ be the Dirichlet convolution of an arithmetic function. Let e(s) = exp{2πis}. Xn and X(n, k)=1 are the relationship between X∞n=1 and X∞(n, k)=1..." Lu Shan explained his ideas, and Poincare listened carefully, taking notes on key points from time to time and giving his own opinions.
The two chatted enthusiastically. Lu Shan was inspired a lot and had his own understanding of the next research.
Time flies, and it is now early December.
It is already winter now. Jiangzhou City is backed by large rivers and has abundant water vapor. The cold wind and cold rain make people's body temperature feel lower than the air temperature.
The trees on the road have lost more than half of their leaves, and the remaining small part is still resisting tenaciously.
But when the wind blew past, after a rustling sound, there were fallen leaves all over the ground again, which looked a little lonely.
The color of the sky is not gray, but a general tone of dark blue, alternating between dark and light, and people's moods change like the sky.
But for those who meet good things, their mood will be sunny no matter how bad the weather is.
For example, everyone in BanSi Company is in a very good mood, and Shenchuan headquarters has just reported on the sales situation for the past month.
In one month, 1 Fuxi K3999s were sold, each at 20 yuan, with a profit margin of 30%. Lu Shan's dividend was 480%, which was million yuan! This was much more than the income brought by Jiyue Company.
Lu Shan's dividend is calculated separately. There is also a lot of profit margin in the part of Shenchuan Company purchasing Bansi C8 memory sticks. Lu Shan has the final say on the money earned from this.
Lu Shan generously took out a portion of the profits to give bonuses to everyone. The past month had been really hard. "The bonus is so high?" Zhang Kaifeng, Liu Wenjie and Zhang Lingxi were all stunned.
"If you think it's too much, just give it back to me?" Lu Shan smiled.
"Thank you, boss!" Liu Wenjie was the first to react and laughed heartily.
Even though Shenchuan sold only 8 laptops this month, the orders actually exceeded 8. Even if Bansi sold only 15 C70s, it would have earned one million. The cost of C is only yuan, and the profit would be yuan.
Apart from the wages of ordinary workers, what does it mean to give each of these key personnel a performance bonus of 30,000 yuan?
"Work hard! You will get more in the future!" Lu Shan encouraged everyone appropriately, because there was really too much work to do later. Who could do such work without giving any encouragement in return?
At this time, Lu Shan thought of the employees of Jiyue Company. Everyone’s salary was actually similar, the only difference was in performance.
Now Jiyue is still in a state of being suppressed, and its performance will be less. After the situation is opened up in the future, its income will definitely not be lower than that of Bansi Company.
Lu Shan is fair, but he is not a pushover. Equal wages are not fair, but a compromise.
In his previous life, Lu Shan saw that the incomes in the Internet and financial industries were abnormally high, but the incomes in the physical manufacturing industry were very low, their status was also low, and even the incomes of scientific researchers were low.
In this life, Lu Shan will not let such a thing happen in his own company. Strength always depends on the physical manufacturing industry, which is the foundation of everything.
Therefore, Lu Shan increased the salaries of manufacturing and scientific research personnel, and the skilled workers in the factory received the highest wages in the market.
Due to the squeeze on orders, the speed of production was not even as fast as the growth rate of orders. Wu Jun rushed to Jiangzhou City with the purpose of completing the expansion of production lines as soon as possible.
"I have already inspected some places in Shenzhen. My production lines will be able to expand soon, and recruiting people will be smooth. I offer high salaries so I am not afraid of not having a job." Wu Jun reported his progress with a cheerful expression, and his expression was almost like saying "I have never fought such a rich battle in my life!"
Lu Shan nodded, and Wu Jun got to the point: "What's the progress of your production line expansion? Do you have a favorite place? Do you want to move to Shenzhen? That would be more convenient."
This time Lu Shan shook his head: "I don't plan to move the production line here to Shenzhen. I have my own reasons. It's a long story."
There are indeed many reasons, the first of which is the problem of scientific research capabilities.
Lu Shan is in Jiangzhou City and can use the equipment of Jiangzhou University and relevant scientific researchers.
Even if we recruit talents in the future, Jiangzhou City is located in the central area of Xia State and has developed transportation, so it won’t take too long for them to come.
If we move to Shenzhen, it will be difficult for the Xiaguo Academy of Sciences to send people over.
Then there is the issue of production equipment. These devices are extremely rare and were all debugged by Lu Shan himself. Some of them were specially customized according to Lu Shan’s requirements.
If there is any accident during transportation, it will be too late to regret.
The last reason is that Lu Shan doesn’t want to leave his hometown. It’s so comfortable to stay in Jiangzhou City. What’s the point of going to other places?
Besides, this is the national logistics center, so it is very convenient to transport goods.
Taking all the above reasons into consideration, the expansion of production lines in the core links can only be carried out in Jiangzhou City.
Wu Jun is not a talkative person. It doesn’t matter if Lu Shan doesn’t go to Shenzhen Stock Exchange, as long as he can supply goods to him.
The memory sticks of BanSi Corporation are very small. A fully enclosed box truck can carry tens of thousands of BanSi memory sticks without causing any delays.
"It doesn't matter, Mr. Lu, you can be wherever you want! I came here to tell you that according to the agreement, I have prepared the revenue of 20,000 notebooks. If you want to use it, just let me know. If the production line needs manpower, just let me know. I will leave after I help you out!"
What Wu Jun meant by this was that he would help but would not leave anyone behind, lest Lu Shan think that he was trying to undermine Ban Si and steal Ban Si's technology.
Lu Shan naturally responded to Wu Jun's kindness: "I can't use so much money all at once. I will take the money in batches, ranging from about 5 million to 10 million each time. You should invest the money in production first."
"It's all up to you." Wu Jun really wanted to take off his hat in salute. If Lu Shan took out 80 million at once, he would have to go to the bank for a loan, and he would have to pay the interest.
Fortunately, Lu Shan is kind and generous, and would not do such a thing. If he were greedy, he might have used the 80 million to do some short-term financial management and earn the interest.
If you are more greedy, facing such a huge cash flow, you may even want to take out some small loans. But that was the end of 2009, and the business completely collapsed from 2012 to 2013.
This time in 2009 was when private lending was booming. The reason was the . subprime mortgage crisis. A large amount of capital fled to China, various investments were hyped up, and there was a shortage of money everywhere.
Not to mention others, Wu Jun had also thought about doing this kind of thing, but fortunately he had some entrepreneurial responsibility and did not do it.
After Lu Shan got the money, he immediately arranged for someone to go through the process.
(End of this chapter)
