universal data

Chapter 317 Conquering the Weak BSD Conjecture
320 chapter

Mathematics master David Hilbert proposed 1900 mathematical problems in his famous speech at the Second World Congress of Mathematicians held in Paris on August 8, 8.

The Hilbert problem has inspired the wisdom of mathematicians and guided the direction of mathematics in the past hundred years. Its influence and promotion on the development of mathematics is huge and immeasurable.

Since the beginning of the 21st century, the Science Advisory Committee of the Clay Mathematics Institute has selected seven "Millennium Prize Questions".

Although the Clay Institute of Mathematics does not have the unique appeal in the mathematics world like Hilbert did more than 100 years ago, it is estimated that there are not many mathematicians in the world who are enthusiastic about the "seven millennium prize questions". I can't solve it, but...they have money!

The Board of Directors of the Clay Mathematics Institute decided to establish a $700 million prize fund, and each "Millennium Prize problem" can be awarded a $100 million reward.

Those top mathematicians may not care about this small amount of money, but among mathematicians, there are a small number of people who live affluent lives and treat money like dung.

So... Countless mathematicians regard these seven millennium mathematical problems as the goals they pursue all their lives.However, 20 years have passed since the Millennium Prize was raised, but among the seven problems, only the "Poincaré Conjecture" has been solved.For the rest, the progress is quite slow.

It is even unknown whether half of the seven millennium prize problems can be solved before the next century.

……

The seven Millennium Prize problems are: NP-complete problem, Hodge conjecture, Poincaré conjecture, Riemann hypothesis, Yang-Mills existence and mass gap, Navier-Stokoe equation, and BSD conjecture.

Obviously, the BSD conjecture mentioned by Professor Fang is also included here.

Facing Professor Fang's question, Cheng Nuo nodded.

As the seven Millennium Grand Prix problems are so famous in the mathematics world, Cheng Nuo obviously has no reason to be unclear.

"I have learned a little bit about the BSD conjecture. The full name is the Poch and Swinnerton-Dayer conjecture."

"The content of the conjecture is: Let E be an elliptic curve defined on the algebraic number field K, E(K) is a set of rational points on E, and it is already known that E(K) is a finitely generated commutative group. Denote L(s, E ) is the Hasse-Weil L function of E. The conjecture says that the rank of E(K) is exactly equal to the order of the zero of L(E,s) at s=1. And the first nonzero coefficient of the Taylor expansion of the latter can be given by The algebraic properties of the curves are precisely formulated."

The BSD conjecture is a complex conjecture, which is incomparable to the simplicity and ease of understanding of the well-known Goldbach conjecture in the mathematics world.

But in the eyes of a mathematician like Cheng Nuo, it was quite easy to understand.

In simple terms, the BSD conjecture describes the connection between the arithmetic properties and analytical properties of Abelian varieties.However, for thousands of years, no one has turned this conjecture into a practical theorem.

"Professor, what are you asking me?" Cheng Nuo asked suspiciously.

Professor Fang smiled slightly, "What if I tell you that I am participating in the proof work of this conjecture?"

"What... what?!" Cheng Nuo opened his mouth wide in surprise.

Professor Fang lowered his hands and said with a smile, "Don't be too surprised. Is it a big deal to prove the seven conjectures? If you can really prove the Millennium Problem, that would be a great achievement."

"What's more, the work I'm doing now is not to prove the BSD conjecture in a broad sense, but the weak BSD conjecture in the case of analytic rank 1."

"The weak BSD conjecture when the analytical rank is 1?" Cheng Nuo lightly chuckled.

"Yes." Professor Fang nodded, and explained, "The BSD conjecture in a broad sense refers to a given Abelian variety on an overall domain, guessing its...free partial volume, the period of all prime sites, and the sand group The exact equational relationship. The first half of it refers to the weak BSD conjecture."

"As early as four years ago, two mathematicians from Yingguo and Deguguo proved the weak BSD conjecture when the analytic rank is 0, and the exact BSD conjecture is valid beyond 2."

"I only started the research on this conjecture two years ago. The current progress... Alas!" Speaking of this, Professor Fang raised the draft paper in his hand and smiled bitterly. A weak conjecture of the conjecture, in two years, I can come up with only a few useful things. For the proof work of the entire BSD conjecture, I am afraid that I have not even completed one percent of the way."

After speaking, Professor Fang handed the draft paper to Cheng Nuo.

Cheng Nuo hesitated for a moment, but didn't take it, "Professor, this is your two years of hard work, let me see... it's not suitable?"

Professor Fang smiled, and stuffed the draft paper into Cheng Nuo's hands, "It's not a confidential document, so you can take it and read it. Besides, the last thing I called you here was related to this BSD conjecture. "

"I want you to be my assistant on the weak BSD conjecture in the case of analytic rank 1, and work together to overcome the weak BSD conjecture!"

Just as Cheng Nuo had just received the drafts handed over by Professor Fang, this thunderous news rang in his ears.

I? BSD guess?

Cheng Nuo's head is a little dizzy now.

This news is actually a bit sudden.

To be honest, Cheng Nuo tried to use his abilities to solve the world's mathematical problems during the period when he obtained the ability, but found that his hardware equipment was really not enough.

A rookie who has not yet graduated from the Novice Village wants to challenge the last big BOSS in the world. Even if he holds a dragon-slaying sword with 999 swords in his hand, he has no power to fight back.So since then, Cheng Nuo has rarely thought about challenging the world's mathematical problems, but has continued to read and accumulate.

Originally, according to the plan, Cheng Nuo was planning to try it again when he graduated from undergraduate, pursued a master's degree, or a master's degree.Unexpectedly, Professor Fang took the initiative to invite himself to join in the work of proving the weak BSD conjecture.

In the past, Cheng Nuo had only solved ordinary mathematics problems, but now he suddenly encountered a thousand-year mathematics problem.

The steps are too big, will it hurt the egg?

"Student Cheng Nuo, classmate Cheng Nuo?"

It wasn't until Professor Fang called into Cheng Nuo's ear several times that Cheng Nuo's thoughts returned to reality.

"Oh, professor, tell me." Cheng Nuo came back to his senses and said.

There was a faint smile on the corner of Professor Fang's mouth, "Student Cheng Nuo, how do you feel about my proposal?"

Cheng Nuo pondered for a few seconds, and finally nodded fiercely, "Do it!"

"Okay." Professor Fang was also quite happy, "Then take these drafts back and have a look, and then we'll talk about the follow-up."

"The work of proving the world's difficult problems doesn't happen overnight, so you don't have to rush as hard as you did in your last project. Just take it step by step."

........................

(End of this chapter)