Chapter 320: Conquer weak BSD conjecture

Chapter 320
The mathematician David Hilbert put forward 23 mathematical problems in his famous speech at the Second World Congress of Mathematicians held in Paris on August 8, 1900.
The Hilbert problem has stimulated the wisdom of mathematicians in the past hundred years, and guided the direction of mathematics. Its influence and promotion on the development of mathematics is huge and immeasurable.
Since the beginning of the 21st century, the Scientific Advisory Committee of the Cray Institute of Mathematics has selected seven "Millennium Award Questions."
Although the Cray Institute of Mathematics does not have the unique appeal of mathematics like Hilbert more than a hundred years ago, even if the "seven thousand-year-old grand prize problem" is proposed, it is estimated that there are not many mathematicians in the world. I am keen to solve it, but...I am rich!
The board of directors of the Cray Institute of Mathematics has decided to establish a seven million dollar award fund, and each "millennium award problem" solution will receive a one million dollar award.
The top mathematicians may not care about this small amount of money, but among mathematicians, there are only a few people who live well and treat money as dung.
Therefore...numerous mathematicians regard these seven millennium mathematics problems as their lifelong pursuit. However, it has been twenty years since the Millennium Award issue was raised, but the only one that has been resolved is the "Poincaré Conjecture". For the rest, progress is quite slow.
Even before the arrival of the next century, it is still unknown whether these seven millennium award problems can be solved in half.
...
The seven Millennium Grand Prize problems are: NP-Complete Problem, Hodge Conjecture, Poincaré Conjecture, Riemann Hypothesis, Yang-Mills Existence and Quality Gap, Navigator-Stork Equation, and BSD Conjecture.
Obviously, the BSD conjecture mentioned by Professor Fang is naturally included here.
Facing Professor Fang's question, Cheng Nuo nodded.
As the seven millennium grand prize question so famous in mathematics, Cheng Nuo obviously has no reason to be unclear.
"I've learned some, BSD conjecture, the full name is Porch and Swinnerton-Daya conjecture."
"The content of the conjecture is: Let E be an elliptic curve defined on the algebraic number field K, E(K) is the set of rational points on E, it is already known that E(K) is a finitely generated commutative group. Let L(s, E) ) Is the Hasse-eilL function of E. It is conjectured that 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 derived from the curve The algebraic nature of is accurately expressed."
The BSD conjecture is a complicated conjecture, and it is incomparable to the conciseness and comprehension of the famous Goldbach conjecture in mathematics.
But in the eyes of a mathematician like Cheng Nuo, it is quite easy to understand.
Simply put, the BSD conjecture describes the relationship between the arithmetic and analytical properties of the Abelian cluster. However, for thousands of years, no one has turned this conjecture into a practical theorem.
"Professor, are you asking me what this is?" Cheng Nuo asked puzzled.
Professor Fang smiled slightly, "What if I tell you that I am participating in the proof of this conjecture?"
"Wh...what?!" Cheng Nuo opened his mouth in surprise.
Professor Fang pressed his hands down and said with a smile, "Don't be too surprised. Prove that there is nothing terrible about the Seven Conjectures. If you can really prove the millennium problem, that would be a great achievement."
"What's more, what I'm doing now is not to prove the BSD conjecture in a broad sense, but to analyze the weak BSD conjecture when the rank is 1."
"Analyze the weak BSD conjecture in the case of rank 1?" Cheng Nuo Qing He.
"Yes." Professor Fang nodded and explained, "The generalized BSD conjecture refers to a given Abelian cluster on an overall domain, guessing its... the volume of the free part, the period of all the elements, and the existence of the sand group. The precise equation 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 analytical rank is 0, and the exact BSD conjecture holds beyond 2."
"I also started the research on this conjecture only two years ago. The current progress... alas!" Speaking of this, Professor Fang Yangyang smiled bitterly on the draft paper in his hand, "The millennium problem is worthy of the millennium problem, although it is only in a broad sense. A weak conjecture of the conjecture, in two years, I can come up with only this useful thing. For the proof of the entire BSD conjecture, I am afraid that even one percent of the road has not been completed."
After speaking, Professor Fang handed the draft paper to Cheng Nuo.
Cheng Nuo hesitated for a moment, but did not take it, "Professor, this is your two years of hard work, let me see... not suitable?"
Professor Fang smiled, and stuffed the draft paper into Cheng Nuo's hands, "It's not a confidential document, just take it and read it. Besides, the last thing I called you is related to this BSD conjecture. "
"I want you to act as an assistant to my weak BSD conjecture in the case of parsing rank 1 and jointly conquer the weak BSD conjecture!"
Just as Cheng Nuo received a few drafts from Professor Fang, this thunderous news rang in his ears.
I? BSD guess?
Cheng Nuo's mind is a little dizzy now.
The news is really sudden.
To be honest, during the time when he got the ability, Cheng Nuo also tried to use the ability to solve the world's mathematical problems, but found that his hardware was not enough.
A rookie who had not graduated from Novice Village wanted to challenge the last world boss. Even if he held a 999 Dragon Slaying Sword, he would have nothing to fight back. So since then, Cheng Nuo seldom thinks about challenging the world's mathematical problems, but keeps studying and accumulating.
Originally, according to the plan, Cheng Nuo was going to try again when he graduated from undergraduate, pursued graduate studies, or master's doctorate. Unexpectedly, Professor Fang would invite himself to join the proof of the weak BSD conjecture.
In the past, Cheng Nuo had dealt with ordinary mathematics small topics, which suddenly came up with a thousand-year mathematics problem.
Too much stride~EbookFREE.me~ Will it be an egg?
"Cheng Nuo, Cheng Nuo?"
It wasn't until Professor Fang called Cheng Nuo repeatedly that Cheng Nuo's thoughts returned to reality.
"Oh, Professor, you said." Cheng Nuo regained consciousness.
There was a faint smile on 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, "Go!"
"Okay." Professor Fang was also very happy. "Then these few drafts, you take them back and have a look, and then we will talk about the follow-up."
"The work of proving the world's problems does not happen overnight, so you don't have to be as desperately in a hurry as you did on the last topic. Gradually, it's better.
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