MTL - The Science Fiction World of Xueba-Chapter 11 BSD conjecture

Kant said positively: "Mr. Pang, I must ask Ms. Say to consider this proposal carefully, but whether it can be implemented will have to be discussed by the UN Security Council."

They are the few human elites who know that the three-body civilization will invade the earth. They have also read the materials of the three-body civilization. In the case that the basic science of the earth has been locked up by the wise son, can they have a human civilization of 400 There was little hope of surviving the war with the trisomy after the year.

But the plan proposed by Pang Xuelin is the first counterattack plan that has made them feel a glimmer of hope for the first time. At the same time, there is a sense of awe for Pang Xuelin, the initiator of this plan.

Pang Xuelin smiled, "Then there is Mr. Laukant."

Next, everyone talked about Adventism for a while.

Xi Pang Xuelin learned from Shi Qiang the reason why he, Fred and Grant were found so quickly.

It turned out that the "Judgment Day" had been spotted by the US military's Virginia-class nuclear submarine before entering the Windward Strait.

They came out of Judgment Day in a lifeboat that night, and they have also been under surveillance of nuclear submarines.

Only after they landed from Cuba and then went into hiding in Santiago did they lose their tracks.

Although Operation Guzheng was successful a few days later, no information about the trisomy civilization was found in the "Judgment Day", and the Adventists disembarking from Port-au-Prince were almost also wiped out by a net. Information for three-body civilization.

踪 The whereabouts of the three of them were taken seriously, and with the active cooperation of the Cuban government, they were quickly located in the bed and breakfast where the three were hiding.

Subsequently, the U.S. military dispatched the "Delta" troops deployed in Guantanamo, preparing to quietly wipe out the three men and one net, but did not expect that the three had an internal strife. Only Pang Xuelin survived.

And in the loft of the guest house, the "Delta" unit also found the burned-out hard disk containing the three-body civilization data.

Originally, the human side had determined that the operation against the "Judgment Day" had failed, and the Adventists had completely destroyed the relevant data of the trisomy civilization.

No one expected that the next day, things would turn around. In the public mailboxes of the five permanent members of the United Nations and the Security Council, I received an email containing all the information of the three-body civilization. The sender was shot by Fred. Pang Xuelin.

Therefore, Pang Xuelin also received the attention of the United Nations. When he was still in a coma, he arrived at the New York University Medical Center through a special plane.

The information that Wu Shiqiang said was not very different from Pang Xuelin's guess. They talked for about another half an hour before the three left.

Xi Pang Xuelin was also relieved. Although the injury was not minor this time, he still achieved the result he wanted.

With the asylum of the United Nations, I can now conduct research in the three-body world with peace of mind.

It is now 2007 in the three-body world. There are still two years to go before the plan of the wall actually begins, which is enough for oneself.

He closed his eyes, called out the system, and began to study the full proof of the BSD conjecture given by the system.

Uh ...

BSD conjecture, full name Bech and Swinarten-Dell conjecture.

Since the 1950s, mathematicians have discovered that elliptic curves are closely related to number theory, geometry, and cryptography.

For example, Wiles proved Fermat's final theorem. One of the key steps is to use the relationship between the elliptic curve and the modular form (Taniyama-Shimura conjecture).

BSD conjecture is related to elliptic curves.

六 In the 1960s, Bech and Swinarter-Dell at the University of Cambridge, England, used computers to calculate rational number solutions to some polynomial equations and found that such equations usually have infinite solutions.

How can we give infinite solutions?

The solution is to classify first. The typical mathematical method is congruence, which is used to obtain the congruence class, that is, the remainder after being divided by a number.

But an infinite number of numbers cannot be needed every time, and mathematicians have chosen prime numbers, so to some extent, this problem is also related to the Riemann conjecture Zeta function.

After a long period of extensive calculations and data collection, Bech and Swinner-Dale observed some laws and patterns, so they proposed the BSD conjecture: Let E be an elliptic curve defined in the algebraic number field K, and E (K) is The set of rational points on E. It is known that E (K) is a finitely generated commutative group. Let L (s, E) be the Hasse-WeilL function of E. Then the rank of E (K) is exactly equal to the order of zero point of L (E, s) at s = 1, and the first non-zero coefficient of the latter Taylor expansion can be accurately expressed by the algebraic nature of the curve.

The first half is usually called the weak BSD conjecture, and the second half is a generalization of the class number formula for the BSD convolution circle domain.

At present, mathematicians have only proved that weak BSD conjectures with rank = 0 and 1 are valid, and there is still nothing they can do about strong BSD conjectures with Rank≥2.

Previously, Pang Xuelin also followed the route taken by Gross and Coates, trying to launch a BSD conjecture with rank ≥ 2 on the basis of rank = 0 and 1, but found that he gradually entered a dead end.

He has not made any progress in the past six months.

Therefore, he was very curious about what ideas were used in the proof process given by the system.

Xi Pang Xuelin opened the BSD conjecture proof and looked at it.

的 The proof of BSD conjecture is more than sixty pages, which seems to be too streamlined for a millennial puzzle level conjecture.

However, this is not important. When Perelman proved Poincaré's conjecture, more than thirty pages were used because the process was too simple and many people couldn't understand it. Under the strong demand of the mathematical community, Pere Herman reluctantly added two more articles, after which he refused to give more.

But this does not prevent Perelman's greatness.

Therefore, the length of the paper is not important, the key depends on the quality of the paper.

Xi Pang Xuelin didn't read from the beginning, but glanced first.

A cursory glance helps him to understand the proof of BSD conjecture as a whole.

However, Pang Xuelin's brow frowned.

的 At the beginning of the thesis, he gave a completely different idea from the current mathematical community.

的 The first part of the thesis is written as a proof of the congruence problem, that is, there are an infinite number of prime factors that are congruences of any specified positive integer.

Then, it is deduced that BSD is true for E_D: D is the product of some 8k + 5 primes and 8k + 1 primes, as long as the 4-fold mapping of the class group of \ BbbQ (\ sqrt {-D}) is single .

This is interesting.

Although in the current mathematical community, some people have tried to prove the BSD conjecture through the congruence problem.

This road is too difficult and is still in its infancy. At present, there are not many achievements in the international mathematical community.

The appearance of this paper shows that the current popular BSD conjecture proof methods will eventually go to a dead end.

证明 Prove the BSD conjecture through the congruence problem, which is the correct idea.

Xi Pang Xuelin held his breath and continued to watch.

Uh ...

Given a prime number p, (1) p \ equiv3 (\ mod8): p is not a congruence but 2p is a congruence; (2) p \ equiv5 (\ mod8): p is a congruence; (3) p \ equiv7 (\ mod8): p and 2p are congruences.

(Weak BSD conjecture) BSD conjecture holds for E_D. In particular, r_D> 0 if and only if L (1, E_D) = 0.

Assuming the weak BSD conjecture holds, (1) theoretically we can determine whether D is a congruence; (2) Tunnell's theorem gives an algorithm to determine whether D is a congruence within a finite step; (3) can prove D \ equiv5, At 6,7 (\ mod8) r_D is an odd number, so such Ds are congruent.

Uh ...

According to the height theory of the Heegner point, the famous Gross-Zagier formula can be related to L '(1, E).

基于 Based on Eichler and Shimura's work on modular elliptic curves and the recently proved Taniyama–Shimura conjecture (modular theorem), L (s, E) can be analytically extended to the entire complex plane and the corresponding Riemann conjecture holds.

Uh ...

At this glance, I don't know how time passes.

I don't know how long it took, Pang Xuelin finally read the whole paper, and he breathed a long sigh of relief.

Although there are still many details and many problems to be solved for this thesis, in terms of the overall proof of thought, Pang Xuelin feels no problem.

And for the proof of the entire BSD conjecture, Pang Xuelin also has a sudden and cheerful feeling.

With the right idea, even without this paper, he can fully derive the proof process of the BSD conjecture.

Xi Pang Xuelin opened his eyes and turned his head to find that it was dark before he knew it. The little blond nurse he had seen before was busy beside him.

Seeing Pang Xuelin's eyes open, she couldn't help but look happy, and said, "God, Pang, you finally woke up!"

Pang Xuelin glanced slightly, glanced over the identity card of the nurse MM, wondered: "Olivia, I ... how long have I slept?"

Olivia said: "You have been sleeping for three days and three nights, and the doctor is still worried about what went wrong. In the past two days, I did a craniocerebral CT and various blood tests. The results show that your You are healthy and healthy, but you just fell asleep, and no one can understand why you sleep so long. "

Xi Pang Xuelin couldn't help but be surprised. Although he had done this in the real world, most of them were interrupted because of the need for sleep and supplementary food. UU reading books www. uukanshu.com

I didn't expect to lie on the bed this time. He actually studied it for three days and three nights, and after waking up, he didn't have the tiredness of bursting liver, but had a kind of refreshing spirit that could not be said.

Did you say that after closing your eyes and entering the system, even if you are doing research in it, it is equivalent to entering deep sleep?

If this is the case, then with the help of the system, my own research efficiency may be improved.

Xi Pang Xuelin's eyes could not help light up.

For a long time, Pang Xuelin didn't think he was a genius. Compared with the famous figures in history, his achievements in academic circles were insignificant.

But Pang Xuelin also has his own pursuit.

He hopes that one day, he can really solve the millennial-level problems with his own strength. He hopes that one day, his name will be comparable to those of the glittering mathematicians in history.

Therefore, he needs to continuously improve his learning and research efficiency.

Maybe in the eyes of others, Pang Xuelin is already a genius, but Pang Xuelin does not think so.

那些 The reason why the so-called genius learners in the world can reach the height of Fengshen is not that he is inherently smarter than others, just because he has good learning habits and efficient learning efficiency.

Not to mention, Pang Xuelin himself can achieve today's achievements because of ten years or one day, more than ten hours of intense study per day.

Even so, he is just a young mathematician who has just emerged in the international mathematics community. There is still a long way to go before the top tycoons.

The genius is one percent inspiration and 99 percent sweat, but there is no 99 percent sweat, where is the one percent inspiration!