universal data

Chapter 333 How Do You Know?
336 chapter

If the solution of the CL2 formula is not a necessary condition, then the subsequent derivation process may not be able to be further optimized...

Inspiration is like love, it comes when you say it!

Countless thoughts collided and flashed in Cheng Nuo's mind.

And what he tried his best to do was to try to catch that flash of inspiration.

Eisenstein series theory?Yes, this is the thing!
This word suddenly popped into Cheng Nuo's mind, and then his whole body trembled slightly with excitement.

What is the Eisenstein series in holomorphic dimension 1 with respect to the non-holomorphic case?To put it simply, it is actually an extension of a special modular shape with an infinite series that can be directly written. The initial definition is a modular group.

In general, let τ be a complex number that strictly affirms the imaginary part.Define the holomorphic Eisenstein series G2k(τ) of weight 2k, where k ≥ 2 is an integer, consisting of the following series:

G2k()=∑1/(m+n)^2k
The absolute convergent holomorphic function τ of this series is in ..The Fourier expansion given below the upper half plane shows that it extends to a holomorphic function, =i∞.
It sounds complicated, but the truth is... this thing is really very obscure.

Cheng Nuo also learned about this systematically and comprehensively in a book discussing "Eisenstein series in holomorphic dimension 1 on the non-holomorphic situation".

At that time, it happened that there seemed to be some marginal relationship between the Eisenstein series theory and the proof of the weak BSD conjecture. However, in previous studies by mathematicians on the BSD conjecture, no one had mentioned what kind of relationship there was between the two.

However, with the mentality of being prepared, Cheng Nuo still kept this knowledge point in his mind.

Unexpectedly, there is actually a time when it can be used.

With inspiration, Cheng Nuo's thoughts immediately diverged.

"Arbitrary holomorphic modular forms of modular groups can be written as polynomials. G4 and G6. In particular, higher order G2k can be written with G4 and G6 via the recurrence relation. Let dk = (2k + 3)k! G2k + 4 For example, d0 = 3G4 and d1 = 5G6. Then dk satisfies the relation ∑(n,k)=2n+9/3n+6..."

“定义q = e2πIτ，G2k()=2λ(2k)(1+……”

"...Bn is the Bernoulli number, ζ(z) is the Riemann Zeta function and σp(n) is the sum of divisors and functions p, then, then..."

The speed of the brain is not fast enough.

Cheng Nuo picked up a blank draft paper, and the formulas appeared on the paper.

In the state of extreme excitement, he has already forgotten the time and fatigue, and only the mathematical formula that is gradually pushing towards the truth is left in his eyes.

Tonight was definitely a sleepless night for Cheng Nuo.

At the same time, in the long history of BSD conjecture research, this is also a night that is enough to be recorded in history!
…………

It was six thirty-five in the morning.

A touch of fish belly white gradually rose in the sky far outside the window.

Cheng Nuo, who stayed up all night, wrote the last line of formula on the scratch paper.

【...N(q)=-1-504∑n^5q^n/1-q^n】

It's finally done!

Cheng Nuo stretched, rubbed his swollen eyes, got up and moved the stool, and poured himself a glass of water.

Professor Fang, who was in a light sleep, was also awakened by Cheng Nuo's voice.

Professor Fang looked up, felt the blanket on his back, and looked at Cheng Nuo.

"Didn't you sleep last night?" Professor Fang asked worriedly, looking at Cheng Nuo's haggard face.

Cheng Nuo nodded.

Professor Fang frowned slightly, "I haven't slept all night, even though you are young, you don't spell it that way! When you get old, you should pay off your body's debt!"

"Professor, I don't often stay up all night. It's okay once or twice once in a while." Cheng Nuo said with a grin.

Professor Fang waved his hand with a smile, "Okay, I know you still have classes in the afternoon. You should go to the dormitory to catch up on sleep. Don't delay your studies because of the work here."

"Understood!" Cheng Nuo received the order, walked to the coat rack by the office door, put on his coat, waved goodbye to Professor Fang, "Then Professor, I will go back to the dormitory first!"

"Yeah. Let's go." Just as Cheng Nuo was about to turn around and leave, Professor Fang stopped Cheng Nuo, "By the way, you stayed up all night to study, did you make any progress!"

"Yes!" Cheng Nuo nodded confidently, and said with a slight smile, "Not only has there been progress, but there has been a lot of progress. The specific things are all on those few draft papers. Professor, you can take a look."

After speaking, Cheng Nuo opened the door and left.

Professor Fang sent Cheng Nuo away, and picked up the four or five draft papers in front of Cheng Nuo's desk full of doubts and began to read.

10 minutes, 10 minutes two, 10 minutes three...

For more than three hours, Professor Fang hardly moved.

Only those slightly trembling fingers showed the extreme unrest in his heart!

Professor Fang gently put the scraps of straw paper back on the table, and leaned back on the chair, tapping the table with his fingers rhythmically, with an extremely gratified expression on his face.

"Cheng Nuo, I hope that the surprises you bring me will become bigger and bigger in the future!"

In the office, Professor Fang's leisurely words sounded.

…………

In the dormitory, Cheng Nuo slept until twelve noon.

While eating the lunch that Yuan Hua helped bring back from the cafeteria, Cheng Nuo swiped through WeChat.

Well, Mu Leng was completely acting like a buddhist girlfriend. He knew that Cheng Nuo was busy, so he didn't send messages to disturb him normally.

It's another girl who has been communicating with Cheng Nuo frequently on wechat recently.

That was Cheng Nuo's new elementary school girl Gong Jiajia, the girl she met at the beginning of school, who also graduated from Qingcheng No. [-] Middle School, but was a year younger than Cheng Nuo.

Originally, Gong Jiajia admired Cheng Nuo, a legendary senior, and after entering university, she even heard some glorious deeds about Cheng Nuo.

For example, I published SCI papers and participated in three or four projects during my freshman year!

It even raised Cheng Nuo's image in Gong Jiajia's mind.

Because Cheng Nuo often sees the beginning but never ends, Gong Jiajia can only ask Tutor Nuo questions on WeChat from time to time.

Cheng Nuo was also out of the idea of ​​being helpful, so he often pointed out a few times when he was free.

Seeing that there was a new message on Gong Jiajia's WeChat icon, Cheng Nuo subconsciously clicked on it. He thought it was a math question, but he didn't expect that he was just asking if he was there.

Gong Jiajia: "Senior, senior, are you there?"

Cheng Nuo: "Yes."

Gong Jiajia: "Senior, do you want to see my photo?"

Hey, are you so unrestrained?

Of course Cheng Nuo refused, "I don't want to watch it."

Gong Jiajia: "Senior, you really don't want to see it?"

Cheng Nuo hesitated for a moment: "Huh? Let's take a look."

Gong Jiajia: "Senior sister is indeed right, the seniors are all wretched men with weak willpower!"

Cheng Nuo: "..."

When did this chick have a convulsion? What is she doing? !

5 minute later.

Gong Jiajia: "Senior, do you want to see my photo?"

Cheng Nuo: "I don't want to watch it."

Gong Jiajia: "Senior, you really don't want to watch it?"

Cheng Nuo: "I don't want to see it!!"

Gong Jiajia: "Hmph, what the senior sister said is really good, the seniors are all a bunch of gays!"

Cheng Nuo: "Wow...wow! How do you know?"

Gong Jiajia: "..."

Another minute passed.

Gong Jiajia: "Senior, I'm sorry, I went to take a shower just now, and it was my roommate who was talking to you. [Poor] [Poor], but, senior, I didn't expect you to not like women."

Cheng Nuo: "..."

(End of this chapter)