Chapter 336

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, like love, 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 grasp the fleeting light.

Eisenstein series theory?yes, that's the thing!

This word suddenly popped up in Cheng Nuo's mind, and then his whole body trembled slightly because of excitement.

What is the Eisenstein series in the holopure dimension 1 In the case of non-hologeneity, it is actually a special modulo with an extension that can be written directly to an infinite series, and is originally defined as a modulo group.

Generally speaking, let τ be a plural and strictly affirm the imaginary part. Define the all-pure Eisenstein series G2k(τ) weight 2k, where k≥2 is an integer and is made up of the following series:

G2k(∂)=∑1/(m+n∂)^2k

The absolutely convergent holopure function τ of this series is in. The Fourier expansion given below the upper plane shows that it extends to an all-pure function, ∂=i∞.

As complicated as it sounds, the truth is...... This thing is really obscure.

It was also in a book that discussed "Eisenstein series in pure dimension 1 about non-pure cases" that Cheng Nuo systematically and comprehensively learned about this knowledge.

At that time, it happened that there seemed to be some relationship between the Eisenstein series theory and the proof of the weak BSD conjecture, but no one in the previous mathematicians' research on the BSD conjecture did not mention the relationship between the two.

However, in the spirit of being prepared, Cheng Nuo still memorized this knowledge point in his mind.

I didn't expect that there would be a time when it could be used.

With inspiration, Cheng Nuo's thinking immediately diverged.

"4 and G6. In particular, higher-order G2k can be used by G4 and G6 through recursive relations. Indulgent dk = (2k + 3)k! G2k + 4 e.g. d0 = 3G4 and d1 = 5G6. Then DK satisfies the relation∑(n,k)=2n+9/3n+6......"

"Define 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 the divisor and functions p, and then ......"

It's not enough to be fast in the brain.

Cheng Nuo picked up a blank piece of scratch paper, and the formulas jumped on the paper.

In a state of extreme excitement, he had forgotten the time, forgot the exhaustion, and all that was left in his eyes was the mathematical formula that gradually pushed towards the truth.

Tonight, for Cheng Nuo, is definitely a sleepless night.

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

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

6:45 a.m.

Outside the window, a touch of fish belly gradually rose in the sky in the distance.

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

【...... N(q)=-1-504∑n^5q^n/1-q^n】

It's finally done!

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

And Professor Fang, who was sleeping lightly, was also awakened by Cheng Nuo's voice.

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

"Didn't sleep last night?" Professor Fang looked at Cheng Nuo's haggard face and asked worriedly.

Cheng Nuo nodded.

Professor Fang frowned slightly, "I haven't slept all night, although you are still young, it is not such a spelling! When you are old, you should pay off your body's debts!"

"Professor, I don't often stay up all night, once or twice once in a while. Cheng Nuo grinned.

Professor Fang smiled and waved his hand, "Okay, I know you still have classes in the afternoon." You should hurry up and make up for sleep in the dormitory, so as not to delay your studies because of work here. ”

"Understood!" Cheng Nuo ordered, walked to the hanger next to the office door, put on his coat, and waved goodbye to Professor Fang, "Then professor, I'll go back to the dormitory first!"

"Hmm. Let's go. Just when Cheng Nuo wanted 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 also been great progress." The specific things are all on those scratch papers, professor, you can take a look. ”

After speaking, Cheng Nuo pushed the door and left.

Professor Fang sent Cheng Nuo away, and with a puzzled heart, he picked up the four or five pieces of scratch paper in front of Cheng Nuo's desk and read them.

Ten minutes, twenty minutes, thirty minutes......

For more than three hours, Professor Fang's figure barely moved.

Only the slightly trembling fingers showed that his heart was extremely unpeaceful!

Professor Fang gently put a few pieces of straw paper back on the table, leaned back on the chair, his fingers rhythmically tapped on the tabletop, and his face showed an extremely relieved expression.

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

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

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

In the dormitory, Cheng Nuo slept until 12 o'clock at noon.

Eating the lunch that Yuan Hua helped bring back from the cafeteria, Cheng Nuo brushed up>Well, Mu Leng's side is completely like a Buddhist girlfriend, and he knows that Cheng Nuo is busy, so he doesn't send messages to disturb him at ordinary times."

is another girl, but she has been frequently > recently, that is Cheng Nuo's new elementary school sister Gong Jiajia, who also graduated from Qingcheng No. 2 Middle School at the beginning of the school year, but is one year younger than Cheng Nuo.

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

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

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

Because Cheng Nuo often sees the dragon without seeing the end, Gong Jiajia can only > Cheng Nuo is also in line with the idea of being helpful, and often points out a few times when he is fine.

Seeing that Gong Jiajia's WeChat icon showed a new message, Cheng Nuo subconsciously clicked in, thinking it was a math problem, but he didn't expect to just ask if he was there.

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

Cheng Nuo: "Yes." ”

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

Hey, is it so unrestrained?

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

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

Cheng Nuo hesitated: "Ah? ”

Gong Jiajia: "What the senior sister said is really right, the seniors are all obscene men with weak willpower!"

Cheng Nuo: "......"

When did this chick have a jerge, what is this doing?!

Five minutes later.

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

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

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

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

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

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

Gong Jiajia: "......"

Another five minutes 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." [Pathetic] [Pathetic], but, senior, I didn't expect you to dislike women. ”

Cheng Nuo: "......"