Omnipotent Data

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 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.

Eisensteinseries theory? Yes, this is the thing!

This word suddenly appeared in Cheng Nuo's mind, and then his whole body trembled slightly because of the 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

This series of absolutely convergent holomorphic functions τ 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 this Eisensteinseries theory and the proof work of the weak BSD conjecture seemed to have some marginal relationship, but no one mentioned the relationship between the two in the previous research on the BSD conjecture by mathematicians.

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.

"4 and G6. Especially high-order G2k can be used 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..."

"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 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 forty-five in the morning.

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

Cheng Nuo, who stayed up all night, wrote down the last line of formula on the draft 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 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 ordered, went to the hanger by the office door and put on his coat, waved goodbye to Professor Fang, "Then Professor, I'll 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.

Ten minutes, twenty minutes, thirty minutes...

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 had brought back from the cafeteria, Cheng Nuo brushed up \u003e Well, Mu Leng's attitude is completely like a buddhist girlfriend. He knows Cheng Nuo is busy, so he usually doesn't send messages to disturb him.

It's another girl who has been frequently seen recently. That's Cheng Nuo's new primary school girl Gong Jiajia, the girl she met at the start of school, who also graduated from Qingcheng No. 2 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, when I was a freshman, I published SCI papers, participated in three or four projects, and so on!

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

Because Cheng Nuo often sees the beginning and the end, Gong Jiajia can only be there from time to time\u003e Cheng Nuo is also out of the idea of ​​being helpful, and often gives advice a few times when he is free.

Seeing that there was a new message displayed on Gong Jiajia's WeChat icon, Cheng Nuo subconsciously clicked in. He thought it was a math problem, but he just asked 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 watch 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? !

five minutes 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 watch 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 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. [Poor] [Poor], but, senior, I didn't expect you to not like women."

Cheng Nuo: "..."