"It's finally done."
When all the equations on the blackboard finally return to the last result.
[L(1,χ)(log D)^2022]
Zhang Yitang, who was standing in front of him, sighed with emotion.
"In general, we proved that the lower bound of L (1, χ) is first related to the distribution of zero points of a type of Dirichlet L-function in a certain area, and derived some results about the gaps between consecutive zero points. Finally, we evaluated some discrete means of large sieve types, and the main one used was your Circle Method Expansion."
About Xiao Yi used Xiao's expansion to introduce the circle method into their problem research, which they temporarily called Circle Method Expansion.
"And now we have also demonstrated that L (1, χ) is too small, thus obtaining an irreconcilable contradiction."
"So - the Landau-Siegel zero point does not exist."
Zhang Yitang turned to look at Xiao Yi next to him, and sighed, "It's over."
His eyes were full of emotion.
His research on this conjecture happened many years ago.
Even earlier than when he studied Twin Prime Conjecture.
In his words, his breakthrough in Twin Prime Conjecture was just the result of a flash of inspiration, and his research on Landau-Siegel-Zero Conjecture has been with him for more than 20 years.
From the time when he was still unknown, he has become a top scholar in the Analytic Number Theory world.
And finally, this question was answered today.
Of course, he knew very well that all this would not be possible without the help of Xiao Yi.
Looking at the young man in front of me...
It really always brings surprises to people.
Xiao Yi nodded slightly and said, "Yes, it's over."
Then he smiled and said, "It's a bit of a pity that it didn't prove to exist in the end. Otherwise, we might have gotten a million US dollars."
As long as it is proved that the zero point exists, it is equivalent to proving that Riemann Hypothesis is wrong.
In this way, you can get the US$1 million provided by Clay Mathematics Institute - Millennium Prize Problems was officially proposed by Clay Mathematics Institute. If you solve any of the problems, you can get the US$1 million reward provided by Clay Mathematics Institute.
Hearing this, Zhang Yitang suddenly laughed and said, "If this is the case, then it is not a pity, but a tragedy."
"Probably the entire mathematical world will be shaken by this."
Once Riemann Hypothesis is proven wrong, quite a few mathematicians may have their lifelong beliefs shattered.
However, Xiao Yi seemed indifferent to this. He shrugged and said, "No matter whether Riemann Hypothesis is correct or wrong, it cannot change just because we want it to be."
"Just like that sentence, objectively existing things are not subject to human will."
"If we really prove the existence of the Siegel zero point, I think the mathematical community should be happy about it."
"After all, this shows that there may be more to our mathematics than we imagine."
Zhang Yitang was startled, then nodded with a smile, "You are right. It's probably like the physics community. If they discover something beyond their experience, they may only be happy."
Hearing what Zhang Yitang said, Xiao Yi, who didn't know much about the physics world, couldn't help but become interested and asked, "Oh? Why is this?"
Zhang Yitang smiled and said, "Two Clouds of Physics, you should know about this."
Xiao Yi nodded and said, "Of course I know, it was mentioned in the high school physics textbook."
Zhang Yitang nodded. "Then those great physicists of the 20th century that you have heard about in textbooks, they all became great physicists because they studied these two dark clouds."
"For example, Einstein, such as Planck, or Fermi, Bohr, these are all like this."
Xiao Yi was startled, but he quickly understood the reason.
"In other words, for the physics community, the more something is beyond their experience, the more it means that something has been hidden that has never been discovered before, which means that some important results can be discovered from it?"
"That's about it." Zhang Yitang raised his eyebrows. Unexpectedly, Xiao Yi reacted very quickly to this kind of thing.
"Now the physics community is lamenting that they have not had a major breakthrough for many years. Of course, these are basically unsolvable things that can be studied. They have been studied in the last century. The problems left for this century are more troublesome than the last."
"For example, it's Vacuum Catastrophe, Dark Matter, Dark Energy, or Black Hole, etc. Going higher, it's the multidimensional universe, String Theory or something like that."
Zhang Yitang laughed and said, "These things sound more sci-fi than the last. With the current level of human technology, it is basically unrealistic to solve these problems. There are things that can be studied, such as something called Higgs Boson. In order to verify whether this particle exists, those physicists spent tens of billions to build a particle collider, which is the LHC."
"Tsk, so, regardless of the fact that among the major majors now, biology, materials and so on have the most research funds. Once those people in physics spend money, they will really die."
Xiao Yi raised his eyebrows, "Sounds interesting."
"You also think it's interesting?" Zhang Yitang smiled, "I used to find it interesting too, but in the end it's still inseparable from mathematics."
"Well... let's just say that the Siegel zero point we have developed now, I think it can be used in physics to verify the theory of the multi-dimensional universe in a few years."
"Siegel probably proved in the 1930s that the Landau-Siegel zero point does not exist in a range that cannot be effectively calculated."
"So there is a saying that through the Siegel zero point problem, we can divide it into two universes. The first universe has a Siegel zero point, and the second universe does not have a Siegel zero point."
"We didn't know which universe we were in before, but now we know that we are in this universe where there is no Siegel zero point."
"Then, in another universe, it exists."
"This question sounds very physical."
"For example, according to the theory of relativity of Einstein, doesn't it mean that compared with the universe we are in, there is another subspace, and all the properties are completely opposite to our universe. Maybe in that space, the mathematical laws are completely changed, so there is a Siegel zero point."
Zhang Yitang shook his head. "Although with our ideas, we can't imagine how the mathematical laws will completely change in another space. Maybe... in another space, from their observation point of view, our Complex Domain is their Real Domain, and our Real Domain is their Complex Domain."
Listening to Zhang Yitang's words, Xiao Yi's brows gradually raised. This kind of completely opposite mathematics?
It sounded even more interesting to him, and he couldn't help but said, "It's probably equivalent to Lobachevskian Geometry?"
"Hmm... almost." Zhang Yitang nodded, "Of course, the difference between the two is quite big. At least Lobachevskian Geometry can still be applied to problems in our world."
Xiao Yi nodded slightly.
The office was slightly quiet for a moment.
Zhang Yitang looked at Xiao Yi's thinking expression, and then said jokingly, "Of course, I'm just talking to you briefly. Don't suddenly become interested in physics and then go to study physics, otherwise..."
"I'm afraid the mathematics community is going to verbally criticize me."
Xiao Yi laughed dumbly, then waved his hands and said, "It's not that bad, not to mention there are still so many unsolved problems in mathematics, my heart is still in mathematics."
Zhang Yitang smiled and said, "Then don't worry about mathematics, but go to physics."
Xiao Yi couldn't laugh or cry, he sounded like a scumbag.
"Okay, let's not talk about these gossips for now. The next step is to organize the paper."
Zhang Yitang took over the matter directly. "Leave it to me to sort out the papers. Maybe Landau-Siegel-Zero Conjecture will be the last major achievement in my life. Let me sort out the papers by myself, which is also a precious memory."
In this regard, Xiao Yi naturally did not refuse and said with a smile, "You have said so, so of course I will not refuse. After all, organizing the paper is quite troublesome, but if you encounter any problems, just come to me."
"OK." Zhang Yitang nodded with a smile.
In the next few days, Zhang Yitang began to compile the paper, while Xiao Yi continued to study the connection between the circle method and Xiao's expansion.
Although there are still many difficulties in further exploring the connection between the two methods, occasionally, Xiao Yi accidentally came up with something new.
"It seems... it's helpful to use this method to decompose prime factors, isn't it?"