NOVEL WEB Chapter 683
Chapter 656 Finite group!
Elliptic curves appear everywhere in modern mathematics. Mathematicians who specialize in other branches have studied elliptic curves. The forerunner was the magistrate Poincaré. This almighty genius scholar who was born in a century first observed in 1901: For each Elliptic curves have a specific group associated with it.
Many scholars have combined group theory to study elliptic curves and have achieved fruitful results.
The elliptic curve theory has attracted the attention of mathematicians thanks to the genius Poincaré, and its prosperity is due to another diligent genius Wiles.
Andrew Wiles used elliptic curve method to prove Fermat’s Last Theorem. He should thank Taniyama Toyoshi and Shimura Goro for their earlier conjectures.
The Taniyama-Shimura conjecture provides an effective way, which is an important step in the proof scheme of Fermat’s Last Theorem.
Wiles first proved the Taniyama-Shimura conjecture, and Fermat’s last theorem was successfully settled by him and Richard Taylor shortly after.
And Taniyama-Shimura Conjecture, one of the proponents of the Taniyama-Shimura conjecture, Taniyama Feng, although he had insight into the secrets earlier than Wiles, but suffered from not being able to prove his own conjecture.
Tani Shanfeng, who was only 31 years old, committed suicide by jumping into the sea on the eve of his wedding. A month later, his betrothed bride committed suicide. This is perhaps the most painful tragedy in the history of mathematics.
Elliptic curve brings not only success and joy, but also failure and sadness.
After more than a hundred years of development, contemporary scholars who study elliptic curves are also mixed with joy and sorrow.
BSD conjectures that this number theory problem is actually transformed into an elliptic curve problem.
Ou Ye is not the first person who thinks of using group theory + elliptic curve to prove the BSD conjecture.
Someone has done this a long time ago, but they didn’t succeed.
The computer screen displays:
L(E,1)≠0→r(E)=0,#Sha(E)＜∞……r(E)=1,#Sha(E)＜∞→ords=1L(E,1)=1 …
#Sha(E) represents the order of the Shafarevih-Tate group of the elliptic curve E. This group is very mysterious. Including the proponents of this group, Shafarevih and John Tate, do mathematicians connect this group? The finite group is not fully understood.
Of course, if you first admit the BSD conjecture, then the Shafarevih-Tate group must be a finite group.
Zhao Tian, Xiaoyun, and Zeng Han were very excited, and the computer check results showed convincingly: Based on the Euye algorithm, the Shafarevih-Tate group is a finite group!
This is undoubtedly a strong evidence to prove the BSD conjecture, and it is an important pre-step!
“This is a small step for us, this is a big step for mankind!”
“Sister Ye Zi Niu batch!”
“Ahahaha, really awesome!”
Zhao Tian and Xiao Yun embraced and celebrated, and Zeng Han, who had always been taciturn, was also very excited.
Why are they so excited, because in their view, the research results their team has achieved at this moment are very close to Andrew Wiles’ proof of the Taniyama-Shimura conjecture before proving Fermat’s Last Theorem.
“The problem that the two great gods Shafalevich and John Tate did not solve was solved by us! Long live Sister Ye Zi! Brother Xiao Zeng, save the results of the calculations and send them to Sister Ye Zi.” Zhao Tian can’t wait to put it. Tell Ou Ye the good news.
Shafalevich is a famous mathematician in the former Soviet Union. His textbooks on algebraic geometry, algebraic number theory, and algebra are one of the first mathematics textbooks introduced to the domestic mathematics majors after the founding of New China. The teachers at the undergraduate level of Ouye are all learning the Shafalevich version of the textbook.
John Tate, an American mathematician, is also a Princeton alumnus of Shen Qi, Ou Ye and Zhou Yu’an. John Tate is the double winner of the Wolf Prize and the Abel Prize. He is a master in the field of algebraic number theory. All he lacks is a Philippine Medal.
Shafarevih and John Tate did not discuss the Shafarevih-Tate group problem, which was clearly demonstrated by Ou Yeh’s manuscripts.
However, for the problems that Birch and Swinnerton-Dale failed to prove, Ou Yeh has not been able to fully prove the problem.
“It’s a pity that the computer can’t verify that the analyst rank is greater than or equal to 2, and the invalid condition. What does this mean… But we thoroughly proved that the elliptic curve with analyst rank equal to 0 and 1 satisfies the BSD conjecture. Xiao Zeng, are the data saved? Send it to Sister Ye Ye!”
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Yan Great People’s Hospital.
Shen Qi stood with his hand in hand, standing in front of the window of the ward.
The rain poured down outside, and the water flooded his car.
Anyway, I bought a safe car insurance.
“This weather is terrible.” Shen Qi vomited. He turned to the hospital bed and stared at the sleeping Ou Ye.
In this clinical trial of the new drug, Ou Ye was arranged to enter the lowest dose group.
The first tolerability test is the lowest-dose group of subjects, and this group has already been done. After a while, the tolerability tests of other dose groups are completed and verified to be safe, and Ouye will return to the hospital to continue the phase I clinical trials of pharmacokinetics/pharmacodynamics.
Shen Qi originally planned to pick up Ou Ye home in the afternoon, but it was stormy outside and the car was flooded, and the couple could not go home temporarily.
DiDi.
Ou Ye’s cell phone sounds a beep.
DiDi.
keep on ringing.
Shen Qi glanced at Ou Ye’s cell phone, which should be messages, emails, etc.
He didn’t dare to look at it, he didn’t dare to ask, his wife’s mobile phone is not allowed to unlock privately, this is iron discipline.
“…” Ou Ye’s lips moved and woke up.
“Leaf, you wake up.”
“Um… It’s raining heavily outside.”
“Heavy rain, quite violent, we will go home again when the rain stops.”
“Okay.” The first thing Ou Ye did after waking up was to touch her phone. She swiped the phone screen to check for new emails and messages.
Message sender Zhao Tian: “Sister Ye Zi, our plan has been verified in the computer room of Shen Qi Research Center. The Shafarevih-Tate group is a finite group. The elliptic curve with analytirank equal to 0 and 1 is in line with our guess! analytirank or algebrairank is greater than or equal to The situation of 2 needs to be further verified. Please check the new email sent to you by Zeng Han! If you can come to the computer room, it will be even better! I wish you a speedy recovery!”
“Yeah!” Ou Ye whispered, very happy.
Shen Qi accidentally glanced at Ou Ye’s mobile phone screen He probably guessed the specific reason why Ou Ye was happy.
“Rank 0 and 1 are done. The Shafarevih-Tate group is indeed a finite group. The two predecessors have very keen intuition.” Ou Ye shook his phone and conveyed good news to Shen Qi.
“That’s great, my wife, you are awesome and invincible.” Shen Qi is happy for Ou Ye from the bottom of his heart. A good mood has an impact on the patient. Of course he is happy to see his wife happy every day.
Ou Ye clicked to open a new email. The sender of the email was Zeng Han: “Sister Ye Zi, please check the attachment. I wish you a speedy recovery.”
The attachments are full of graphics and table data, and Ou Ye will check them carefully.
After reading it, Ou Ye suddenly became less happy. She handed the phone to Shen Qi: “If the rank is greater than or equal to 2, there is no one byte of verification data. I think I should have overlooked an important link.”
Shen Qi took the mobile phone and quickly calculated and analyzed, and said: “According to your settings, the initial computer verification, for the case of rank greater than or equal to 2, you should at least get the verification data after Taylor expansion. You may indeed ignore it. A certain key link has been reached, but you have done well. Yo, the rain has stopped, let’s go home, and study it slowly when we get home.”
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(July 1st, the party’s birthday, please guarantee the monthly pass!)