I really just want to be a scholar

Chapter 398 Matching Approximation Method in Geometric Number Theory

After a brief chat with Ning Qingyun, Qin Ke's mood suddenly brightened. He shook his head, put his mind away and sat down at the desk, opened the notes he made during today's report, and reviewed them again.

This knowledge is recorded by himself, not directly instilled by the system. It is easy to forget after a long time. He must fully understand it and integrate it into his own knowledge system before it can be truly used by him.

In about half an hour, Qin Ke had digested all the contents of the note and looked at the system interface.

"Mathematics level: professional level, next level: master level, upgrade progress: 576/1000".

Not bad, I earned 45.5 points of mathematics academic points in one day today.

Qin Ke continued to delve into the "function transformation hypergeometric system" and "group theory function equation method" happily. He had a vague intuition that one of these two mathematical methods must be the key to cracking Polignac's conjecture .

Time passed by like this bit by bit, and Qin Ke's cell phone vibrated suddenly.

Qin Ke immediately put down his pen and picked up his phone. Sure enough, it was Ning Qingyun who made the video call.

Click to connect to the video, and Ning Qingyun's familiar pretty face appeared on the screen.

Fair and tender skin, exquisite and perfect facial features, a pair of phoenix eyes rippling with gentle and shy water waves, and the high ponytail made Qin Ke's mood jump up all of a sudden. He pressed down and wanted to kiss the screen. The impulse of a kiss, said with a smile: "Morning, Yun'er."

When Ning Qingyun saw Qin Ke's "disgusting look" on his hippie smiling face, he suddenly remembered the two words he had accidentally written, his face blushed immediately, and he said angrily, "You...what are you laughing at?"

"Seeing my Yun'er happy, why, don't you laugh?"

"Laugh if you want, you're a bad guy anyway..." Ning Qingyun seemed to be walking around, raising her head to look at the road from time to time, but when her eyes fell on the screen, a sweet smile appeared.

"You just finished lunch?"

"Well, I just left Yanfei and the others, and now I'm on my way to 'Xiaowo No. [-]'."

Qin Ke heard it keenly. Ning Qingyun sent a video request just after he separated from his roommates. Obviously, he couldn't wait to come back to video with him in the study room.

Thinking of the young girl's longing and love that was also fermented by the parting, Qin Ke felt even sweeter in his heart, and he said softly: "'Xiaowo No. [-]' is far away from the girls' dormitory building, and it is a bit quiet. Don't go alone."

"I know, you're not here, and I don't dare to stay there alone at night. I have been acting with Yan Fei and the others these days, and I also go to the library to study at night. You don't have to worry about me. You are here In a foreign country, please pay attention to safety.”

"Hey, I'm also safe here. By the way, you said you have an idea to prove Zhou's conjecture?"

"That's right." Ning Qingyun's star-black eyes suddenly shone with joy:

"I have been studying the 'Matching Approximation Method of Geometric Number Theory' that you taught me recently, but I still can't figure out how to use it to prove the Polignac conjecture. On the day you left for Princeton, I went to the library with Yan Fei and the others Self-study, when I was helping Xiaohui find a book, I accidentally found a book about Zhou's conjecture."

The girl's single ponytail flicked lightly, she was indescribably cute: "I looked at it for a while, and suddenly I had an idea. The 'matching approximation method of geometric number theory' is a very excellent mathematical method specially used to solve number theory problems. I I haven’t been able to apply it to the Polignac’s conjecture for the time being, so can it be applied to the Zhou’s conjecture?”

Qin Ke's heart moved, yes, he is really a fan of the authorities, and he has been only staring at Polignac's conjecture in order to complete the system's tasks. Why didn't he think that these new mathematical methods could be used to prove other conjectures?

I only heard Ning Qingyun say in a slightly proud tone: "So I have been working hard in this direction for the past three or four days, and I have made a lot of progress. I have written out all the ideas I can think of this morning. Unfortunately, there are still a few key changes that I can't figure out, so I need you to perfect them."

Qin Ke smiled and said, "The more you talk about it, the more curious I become."

"Wait a little longer, I'll run faster."

"Don't worry, don't fall down."

Ning Qingyun murmured slightly: "I'm not a child, how could I fall so easily?"

Qin Ke looked at her girlish posture that would only be shown in front of him, and couldn't help being happy: "In my impression, you seem to have fallen down several times, I don't want you to accidentally fall, there is something wrong Boys from all over the world came to save the beauty as a hero."

Ning Qingyun pursed her lips and smiled lightly, her eyes were looking forward, the water was rippling, and she was a little more charming: "I won't let other boys touch me, even if I fall, I will get up by myself. Let me ask you Ah, I always fell down when I was with you before, did you deliberately make trouble?"

Qin Ke smiled: "Guess?"

"Hmph, scoundrel, I guess it must be, you've been full of bad ideas, trying to make me like you all day long." Ning Qingyun wanted to put on a stern face, but when she thought of the past, she couldn't help laughing, with a frown on her face. All happiness.

The two of them just chatted without saying a word, without any theme, but it felt that even the air became sweeter.

When she arrived at the "Xiaowo No. [-]" self-study room, Ning Qingyun quickly put down her schoolbag, took out a notebook and opened it, on which several pages were filled with beautiful handwriting.

"Okay, I'm going to start explaining my proof ideas." The girl pointed the phone camera at the page of the notebook, and pointed to the mathematical formula above with her tender little finger:
"Zhou's conjecture, I think you must be familiar with it. I saw that you have read the relevant information before, so I won't go into details. You see, my idea is that we can start by setting k=2n, and 2n must be is an even number..."

The notebook flipped through the pages.

Ning Qingyun's voice could not conceal his excitement: "Look, at this point, we can basically transform it into a problem of algebraic geometry through the 'matching approximation method of geometric number theory', and then use the quadratic model of the objective function in This linearized approximation of (k, n), making an effective algebraic approximation, can further open up the mind..."

Ning Qingyun spoke for nearly 10 minutes in one breath, and then said a little embarrassedly: "Then I am not sure how to proceed here, and my idea is to make another mathematical assumption here, using Banach space theory to I can't think of how to get it. Do you think my way of thinking is right?"

Qin Ke's eyes lit up when he heard it. Ning Qingyun's idea was very delicate. It was obvious that she had thoroughly researched the "matching approximation method of geometric number theory" and used it very skillfully. That's why she came up with such an idea to prove Zhou's conjecture. The key is that she can The idea of ​​using Banach space as a bridge shows that she has fully mastered the "Zhining Qingyun II" number theory knowledge system tailored for her by Qin Ke.

Qin Ke closed his eyes and meditated for a while, then took a pen and wrote more than a dozen lines of calculations, finally raised his head, and showed a bright smile to Ning Qingyun who was looking at him anxiously on the other side of the phone:
"You are amazing, Jun'er! Your thinking is completely fine!"

He moved the scratch paper to the front of the camera: "Look, I propose to establish a Banach space here, and then take any x∈X, as long as it is proved that there is an optimal approximation element in the non-empty closed convex set, we can combine these The approximation elements are matched one by one, and then it is proved that the equation system of this algebraic geometry figure has a definite solution! This proves that Zhou’s conjecture is true under the condition that we set k as an even number earlier!”

Ning Qingyun's eyes glowed with admiration, and Qin Ke figured out the problem that had troubled her for a long time, and it took only a few minutes for her to figure it out!

This Qin Xiaoke is really a super super super math genius.

The girl lowered her eyes so that Qin Ke would not be complacent when she saw her adoring eyes, and asked again: "Then the proof that k is an odd number..."

"The proof of the condition that k is an odd number is much less difficult. It is almost the same as before. Make some changes in the No. 19 step you mentioned just now. Through the affine transformation of two-dimensional homogeneous coordinates, a set of invariants is used for translation. and reflection, turn it into an algebraic geometry problem, and then use the approximation matching method, it should be able to prove it!"

"That is to say," Qin Ke's tone was affirmative and excited: "Yun'er, Zhou's conjecture, we can prove it in our hands soon!"

"Us? But I just provided an idea, and it's just a two-thirds proof idea under the condition that k is an even number..." Ning Qingyun knew in his heart that although he had come up with some ideas, he wanted to turn them into The specific demonstration process is very difficult, at least she has no confidence to write it out.

"Of course, this is the result we made together. Without your ideas, I wouldn't be able to prove it in two years! This is a project we did together, called 'Qin Ke and Ning Qingyun's Zhou's Conjecture Proof Project' All right!"

Ning Qingyun felt sweet in her heart. Qin Ke's approval and affirmation made her finally feel that she could stand beside him with her head held high.

I am not only being pulled forward by him, but also giving him some boost.

This filled Ning Qingyun with a sense of accomplishment and joy.

"Jun'er, in the past two days, try to write out the proof process of Zhou's conjecture according to the ideas I just completed. This will be very helpful to improve your mathematical ability."

"But... I'm afraid that I won't be able to finish the whole argumentation process..."

"It doesn't matter, write down everything you can, and leave the rest to me. I... try to follow your train of thought and see if you can prove a few more conjectures using the 'matching approximation method of geometric number theory'! Polignac guesses that we will not touch this kind of big BOSS for the time being, and use the other small BOSS to deal with it first, accumulate more experience points, and deal with it after leveling up!"

Ning Qingyun looked at his confident and arrogant expression, couldn't help pursing his lips and said with a smile: "You thought it was playing games, and you need to save some experience points to upgrade."

Qin Ke smiled. For him, what he accumulates is not experience points, but academic points, but they can indeed be upgraded.

He remembered what he had seen and heard in Princeton University yesterday, took a deep breath, and said firmly: "Jun'er, come on, we both have to work hard to figure out a few small conjectures together, let those foreigners who look down on us Xia Guo see, we The mathematicians of the Xia Kingdom are not inferior to the mathematicians of any other country!"

"En." Ning Qingyun lowered her eyes again, every time she saw such a confident and domineering Qin Ke, she would have the urge to kiss him.

"By the way, you... have to go to bed early, it's already one o'clock in the morning on your side."

Qin Ke blinked: "Okay, but you have to kiss me first."

Ning Qingyun blushed again: "Kiss... I can't kiss."

"Is it okay to 'Mua'? Or 'Baji'."

Ning Qingyun shook her head vigorously: "I...I won't..."

Qin Ke's face was sloppy: "I won't learn it now. Anyway, if you don't kiss me, I won't sleep. I will go to the report meeting tomorrow with my panda eyes and yawning, and then maybe I will be at the meeting again." Falling asleep and snoring, being kicked out of the venue and being humiliated...... Do you feel distressed when you think about it this way?"

"...Bad guy." Ning Qingyun blushed and tapped the screen with her slender little finger.

"Hey, Yun'er..." Qin Ke still wanted to fight, but the video was cut off.

Qin Ke: "..."

Well, it seems that I have gone too far in teasing this extremely tender-skinned girlfriend.

He put down his phone, went to brush his teeth and rinsed his mouth, and was about to go to bed when he accidentally found an extra message on his phone.

Open it and see that it is the voice from Ning Qingjun.

There are 56 seconds.

Qin Ke's heart skipped a beat and he clicked play.

As a result, there were always rustling noises inside, and it was almost 40 seconds before I heard a small, weak girl's voice saying:

"I...I tried many times, but I can't make the sounds of 'Mua' and 'baji'... Anyway, I kissed you, you are going to bed soon! Good night!"

Qin Ke burst out laughing, isn't his girlfriend too cute?Imagining Ning Qingyun's flushed face at this time, Qin Ke laughed and rolled on the bed a few times, then picked up the phone, and sent "Mua" vigorously.

"Good night, my dear little cabbage."

I love you so much.

　First send two updates of 6K6, and there will be a chapter of 3KR in the evening, and today I will be owed an update every day, and continue to ask for monthly ticket recommendations, Zhang said.

　　In addition, the VIP reminder group has benefits, welcome to join!

　　Finally, I would like to recommend a great book, "The Museum of Demon Town", a fire book with good grades, if you are interested, go check it out!

　　
　
(End of this chapter)