Chapter 333 (1/2)
Chapter 336
if the solution of Cl2 formula is not necessary, then the subsequent derivation process can not be further optimized
Inspiration, just like love, is coming!
Countless ideas collide and flash in Cheng Nuo's mind.
And what he tried to do was to grasp the flash of light.
Eisensteinseries theory? Yes, that's it!
Cheng Nuo's mind suddenly came up with this word, and then his whole body trembled slightly because of excitement.
What is Eisenstein Series in holomorphic dimension 1 with respect to the non holomorphic case? In short, it is a special module with the extension of infinite series that can be written directly. The original definition is a module group.
Generally speaking, let τ be a complex number and strictly affirm the imaginary part. In this paper, we define the weight 2K of the Holomorphic Eisenstein series g2k (τ), where k ≥ 2 is an integer, which is composed of the following series:
g2k (∂) = ∑ 1 (M + n ∂) ^ 2K
the holomorphic function τ of this series is absolutely convergent. The Fourier expansion given below the upper half plane shows that it extends to a holomorphic function, ∂ = I ∞.
it sounds complicated, but in fact This thing is really very obscure.
Cheng Nuo is also in a discussion of ”the Eisenstein Series in holomorphic dimension 1 about the non holomorphic case”, only then systematically and comprehensively understood about this knowledge.
At that time, it happened that the proof of the eisensteinseries theory and the weak BSD conjecture seemed to have some marginal relations. However, in the previous studies on BSD conjecture, no one has mentioned the relationship between the two.
However, in the spirit of preparedness, Cheng Nuo or put this knowledge point in mind.
I didn't expect that it could be used.
With inspiration, Cheng Nuo's thinking immediately spread.
Any holomorphic modular form of a module group can be written as a polynomial. G4 and G6. In particular, G4 and G6 can be used as recursive relations for high-order g2k. For example, g2k = g2k + 4. Then DK satisfies the relation ∑ (n, K) = 2n + 93n + 6... ”
”Definition q = E2 π I τ, g2k (∂) = 2 λ (2k) (1 +...”
“…… BN is a Bernoulli number, ζ (z) is a Riemann zeta function and σ P (n) is the sum P of divisors and functions, then... ”
The brain is not fast enough.
Cheng Nuo picked up a blank draft paper, a formula leaping on the paper.
In a state of extreme excitement, he has forgotten the time, forgotten fatigue, and in his eyes, only the mathematical formula gradually pushed to the truth is left.
Tonight, for Cheng Nuo, it's definitely a sleepless night.
At the same time, in the long history of BSD conjecture research, this is enough to be recorded in the history of one night!
…………
It's six forty-five in the morning.
Out of the window, a touch of white fish belly gradually rises in the sky.
Cheng Nuo, who stayed up all night, wrote down the last line of formula on the draft paper.
【…… N (q) = - 1-504 ∑ n ^ 5q ^ n1-q ^ n]
finally it's done!
Cheng Nuo stretched, rubbed some bulging eyes, got up, moved the stool and poured himself a glass of water.
And the shallow sleep Professor Fang 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 looked at Cheng Nuo's haggard face and asked anxiously.
Cheng Nuo nods.
Professor Fang frowned gently, ”I haven't slept all night. Although you are still young, it's not the spelling! When you're old, you should pay for your body! ”
”Professor, I don't always stay up all night. It doesn't matter once or twice.” Cheng Nuo said with a smile.
Professor Fang waved his hand with a smile, ”OK, I know you still have classes in the afternoon. You can make up your sleep in the dormitory as soon as possible. Don't delay your studies because of the work here. ”
”Understand!” Cheng nuodeling went to the hanger beside the office door, put on his coat, waved goodbye to Professor Fang, ”then Professor, I will go back to the dormitory first!”
”Well. Let's go. ” When Cheng Nuo was just about to turn around and leave, Professor Fang stopped Cheng Nuo, ”by the way, you stay up all night studying. Have you made any progress?”