The Science Fiction World of Xueba

Kanter said seriously: "Mr. Pang, I must ask Ms. Say to consider carefully the plan you proposed, but whether it can be implemented will have to be discussed by the UN Security Council."

These few people are among the few human elites who know that the Three-Body Civilization will invade the earth, and have read the materials of the Three-Body Civilization. With the basic science of the Earth locked up by sophons, they have no idea whether human civilization can survive within four hundred years. There is little hope of surviving the war with the Trisolarans years later.

But the plan proposed by Pang Xuelin was the first counterattack plan that made them feel a glimmer of hope so far. At the same time, they also felt a little awe of Pang Xuelin, the proposer of this plan.

Pang Xuelin smiled and said, "Then there is Mr. Laucante."

Next, everyone chatted for a while about Adventism.

From Shi Qiang, Pang Xuelin got the reason why he, Fred and Grant were found so quickly.

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

That night they got out of the Judgment Day in a lifeboat and have been under the surveillance of the nuclear submarine.

It was only after they landed from Cuba and then went into hiding in Santiago that they lost track of them.

Although the "Operation Guzheng" was successful a few days later, no relevant information about the Trisolaran civilization was found in the "Judgment Day", and the Adventists who disembarked in Port-au-Prince were almost wiped out. Information about the Trisolaran civilization.

The whereabouts of the three of them were paid attention to, and with the active cooperation of the Cuban government, the homestay where the three were hiding was quickly located.

Afterwards, the U.S. military dispatched the "Delta" troops deployed at Guantanamo Bay, intending to quietly wipe out the three of them, but they did not expect that the three had internal strife, and only Pang Xuelin survived.

Moreover, in the attic of the hotel, the "Delta" troops also found a hard drive that had been burned and stored the materials of the Trisolaran civilization.

Originally, the human side had already determined that the operation against the "Judgment Day" had failed, and the Advent faction had completely destroyed the relevant materials of the Trisolaran civilization.

No one expected that things would turn around the next day. In the public mailboxes of the five permanent members of the United Nations and the Security Council, an email containing all the materials of the Three-Body Civilization was received, and the sender was shot and injured by Fred. Pang Xuelin.

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

The information Shi Qiang said was not much different from what Pang Xuelin had guessed. After chatting for about half an hour, the three of them left.

Pang Xuelin also breathed a sigh of relief. Although the injury was serious this time, he still achieved the result he wanted.

With the protection of the United Nations, I can then conduct research in the Trisolaran world with peace of mind.

It is now the year 2007 in the Three-Body World, and there are still two years before the wall-facing plan is actually implemented, which is enough to make waves on your own.

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

...

The BSD conjecture, the full name of the Behe ​​and Swinton-Dell conjecture.

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

For example, when Wiles proved Fermat's last theorem, one of the key steps was to use the relationship between elliptic curves and modular forms (Taniyama-Shimura conjecture).

The BSD conjecture is related to elliptic curves.

In the 1960s, Beh and Swinton-Dell of the University of Cambridge in the United Kingdom used computers to calculate the rational number solutions of some polynomial equations and found that such equations usually have infinitely many solutions.

But how to give infinitely many solutions?

The solution is to classify first,

The typical mathematical method is congruence and thus the congruence class, that is, the remainder after division by a number.

However, it is impossible for infinite numbers to be needed, so mathematicians choose prime numbers, so to some extent, this problem is also related to the Riemann Hypothesis Zeta function.

After a long period of calculation and data collection, Bech and Swinton-Dell observed some laws and patterns, and thus proposed the BSD conjecture: Suppose E is an elliptic curve defined on the algebraic number field K, and E(K) is The set of rational points on E, we know that E(K) is a finitely generated commutative group. Note that L(s, E) is the Hasse-Weil L function of E. Then the rank of E(K) is exactly equal to the order of the zero point of L(E, s) at s=1, and the first non-zero coefficient of the Taylor expansion of the latter can be precisely expressed by the algebraic properties of the curve.

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

At present, mathematicians have only proved that the weak BSD conjecture of rank=0 and 1 is established, and they are still helpless for the strong BSD conjecture of Rank ≥ 2.

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

In the past six months, he has not made any progress.

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

Pang Xuelin opened the BSD conjecture proof paper and read it.

The proof of the BSD conjecture has a total of more than sixty pages, which is too streamlined for a conjecture at the level of the Millennium Puzzle.

But this is not important. When Perelman proved the Poincaré conjecture, it only took more than 30 pages. Because the process was too simple, many people could not understand it. Under the strong request of the mathematics community, Perelman Erman reluctantly added two more articles, and then refused to give more.

But that doesn't stop Perelman from being great.

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

Pang Xuelin did not read carefully from the beginning, but browsed roughly first.

A rough browsing will help him understand the proof ideas of the BSD conjecture as a whole.

But soon, Pang Xuelin frowned.

At the beginning of the paper, a completely different idea from the current mathematics circle is given.

The first part of the paper is written about the proof of the congruence number problem, that is, there are infinitely many congruence numbers whose prime factors are any specified positive integers.

Then, deduce that BSD holds for such E_D: D is the product of some 8k+5 type prime number and some 8k+1 type prime numbers, as long as the 4-fold mapping of the group of \\Bbb Q(\\sqrt{-D}) is simple of.

That's where it gets interesting.

Although in the current mathematics community, some people have tried to prove the BSD conjecture through the congruent number problem.

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

The emergence of this paper shows that the current popular BSD conjecture proof method will eventually lead to a dead end.

Proving the BSD conjecture through the congruent number problem is the correct way of thinking.

Pang Xuelin held his breath and continued to read.

...

Given a prime number p, (1)p \\equiv 3(\\mod 8): p is not a congruence number but 2 p is a congruence number; (2)p \\equiv 5(\\mod 8): p is a congruence number; (3) p \\equiv 7(\\mod 8): Both p and 2 p are congruent numbers.

(Weak BSD conjecture) The BSD conjecture holds for E_D. In particular, r_D\u003e0 if and only if L(1, E_D)=0.

Assuming that the weak BSD conjecture is true, then (1) theoretically we can determine whether D is a congruent number; (2) Tunnell's theorem gives an algorithm to determine whether D is a congruent number within a finite step; (3) it can be proved that D \\equiv 5 , 6, 7(\\mod 8) when r_D is an odd number, so such D is a congruent number.

...

According to the height theory of Heegner point - the well-known Gross-Zagier formula can relate it to L'(1, E).

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

...

When you look at it, you don't know the passage of time.

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

Although there are still many details and problems to be solved for this paper, Pang Xuelin feels that there is no problem with the overall proof idea.

And for the proof of the entire BSD conjecture, Pang Xuelin also felt a sense of enlightenment.

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

Only then did Pang Xuelin open his eyes, and when he turned his head, he found that it was already dark before he knew it, and the little blond nurse he had seen before was busy beside him.

Seeing Pang Xuelin open her eyes, she couldn't help showing joy, and said, "My God, Pang, you finally woke up!"

Pang Xuelin froze for a moment, glanced at the nurse MM's ID card, and asked in confusion: "Olivia, I... How long have I been asleep?"

Olivia said: "You have been sleeping for three days and three nights, and the doctor is still worried that something is wrong with you. In the past two days, they have performed brain CT and various blood tests on you. The results show that your In good health, just asleep, no one can explain why you sleep for so long."

Pang Xuelin couldn't help being surprised. Although he had done this kind of liver explosion research in the real world, most of them were interrupted because of the need for sleep and food supplements.

Unexpectedly, lying on the hospital bed this time, he actually studied for three days and three nights, and after waking up, he didn't feel that exhausted, but instead felt refreshed.

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

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

Pang Xuelin's eyes lit up involuntarily.

For a long time, Pang Xuelin did not think that he was a genius. Compared with those famous figures in history, his achievements in academia were insignificant.

But Pang Xuelin also has his own pursuit.

He hopes that one day, he can truly solve millennium-level problems with his own power, and that one day, his name can be compared with those shining mathematicians in history.

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

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

The reason why those so-called geniuses in the world can reach the height of conferring gods is not because they are naturally smarter than others, but because they have good study habits and high learning efficiency.

Among other things, the reason why Pang Xuelin himself can achieve today's achievements is because of the ten-year-long high-intensity study of more than ten hours a day.

Even so, he is only a young mathematician who has just shown his talents in the international mathematics community, and there is still a long way to go before those top talents.

Genius is one percent inspiration plus ninety-nine percent sweat, but without ninety-nine percent sweat, where does that one percent inspiration come from!