The literature that caught Chen Zhou's eye was another tool in the field of number theory research.

That is, the circle method.

It and sieve methods have always been the two most important methods in the field of number theory research.

Of course, in addition to the sieve method and the circle method, there are also methods such as density.

The full name of the circle method is the Hardy-Littlewood-Ramanujan circle method.

The names are the British mathematician Hardy, the British mathematician Littlewood and the Indian mathematician Ramanujan.

Of these three people, Chen Zhou is not a stranger.

Ramanujan, whose outstanding contribution to mathematics, was so great that in India, along with Mahatma Gandhi, the poet Rabindranath Tagore, and others, he was called the "son of India".

Moreover, there are now two mathematics prizes named after Ramanujan internationally.

Hardy and Littlewood, both British mathematicians, have made outstanding research in Diophantine diagram analysis, stacked number theory, integrative number theory, trigonometric series, etc.

And together they completed a new proof of Hualin's theorem.

When it comes to trigonometric series, the Fourier series is a type of trigonometric series.

As for the relationship between the three, in Hardy's words, his greatest achievement in mathematics was "the discovery of Ramanujan."

It was with Hardy's help that Ramanujan gradually rose to prominence as a mathematician.

Speaking of Hardy.

In a sense, it can be said that he influenced the thinking of a generation of mathematicians in China.

The reason why Huaguo will achieve "1+2" in number theory, or in the Goldbach conjecture, is that Mr. Chen has achieved "1+2".

In fact, it has a little to do with Hardy.

Mr. Chen's teacher is Mr. Hua, and Mr. Hua's teacher is this Hardy.

It's just that Mr. Chen advanced the Goldbach conjecture to "1+2" and used the weighted sieve method, not the circle method.

The circle method was originally invented by Hardy and Littlewood in the theory of stacked prime numbers.

Then, they realized that it seemed to have something to do with Goldbach's conjecture.

So he perfected the theory of the circle method and gave a method, a way to describe the thing "There is a method of dismantling" in mathematical language.

That is, through the circular method of the iconic integral formula.

【∫01e^(2πimα)dα】

Considering this integral, m=0, ∫01e^0dα=1.

m≠0, the exponent cannot be 0, and according to Euler's formula, the whole power becomes 0.

So the whole integral is 0.

Using this property, it is possible to transform the integral into a splitting function.

Each N=p1+p2,p1,p2≥3 split can be written as D(N)=∫01(2

In the same way, the splitting method of N=p1+p2+p3,p1,p2,p3≥3 can be written as T(N)=∫01(20 and T(N)>0 for N that arbitrarily satisfies the question.

At this point, it's time to start talking about points.

This is the main idea of the "circle method".

The essence of the circle method is the Fourier analysis applied to number theory.

To put it simply, it is to analyze the functions on the circumference.

On the other hand, the purpose of sieving the heads and tails of a coin is to give an approximate estimate of the distribution of prime numbers.

"Since the way of the sieve method may not work, then try the circle method......

Chen Zhou thought in his heart, but the movements in his hands were not in a hurry.

He began to search for literature related to the circular method.

If you want to do a good job, you must first sharpen your tools.

For the use of the circle method, Chen Zhou has not completely understood.

Not to mention, it will be used immediately to solve the correction problem of the Kramer conjecture.

Chen Zhou's eyes were unusually bright, and there was a hint of expectation in his eyes.

Staring at the computer screen in front of him, absorbing the knowledge content on it, to enrich his own knowledge.

In fact, in addition to the sieve method and the circle method, there are many small skills in the field of number theory.

The generalized Riemann conjecture, for example, can be used to prove some limited special cases.

And then use these special cases to prove something else.

It's like the so-called "zero-point zone".

Although it is not yet known how to prove that the real part of all non-trivial zeros is 1/2.

But it has already been shown that the zero point must be in some region containing the so-called "critical line", which is very small near the real axis.

Since then, similar conclusions have been used to prove other problems.

It's just that Chen Zhou doesn't like this method very much.

Because he always finds it a little strange to use an unproven conjecture to solve another conjecture.

What if the Riemann conjecture is falsified?

Even if this probability is very small, even if there are already thousands of mathematical problems solved by relying on the Riemann conjecture, Chen Zhou is still reluctant to try.

He still wants to step on every step steadily.

Of course, if one day, he can prove the Riemann conjecture.

That's a different story.

Time slowly moved forward, and Chen Zhou had already started the actual battle after brushing up several documents.

Yang Yiyi on the side looked at the content that Chen Zhou wrote on the scratch paper with some curiosity.

It's just that she read it once, but she didn't understand it too much.

Yang Yiyi naturally didn't plan to study it in depth, she was just attracted by Chen Zhou's state.

It's a bit familiar......

How to put it, it's like ......

It's like the feeling the last time Chen Zhou solved the hail conjecture.

Could it be said?

Yang Yiyi, who was thinking like this, had a hint of surprise in her eyes.

She remembered that the last time she heard Chen Zhou say that he was studying the Crummel conjecture, which seemed to be a mathematical problem that had plagued the mathematical community for nearly a hundred years, right?

Is it going to be solved so soon?

Yang Yiyi just looked at Chen Zhou like this, and was a little distracted for a while.

Chen Zhou is devoting himself to studying how to use the circle method to solve the correction problem of Clamell's conjecture.

As he looked at the literature, there was a moment when he felt like he had grasped that fleeting inspiration.

However, as time went by, he felt more and more that this problem was really difficult......

There is no doubt that he did not grasp the inspiration of that moment.

He also failed to resolve the amendment.

Slowly, the speed at which the pen in Chen Zhou's hand rubbed against the scratch paper slowed down.

Chen Zhou's originally bright eyes also became a little confused.

His eyebrows were already wrinkled together.

"Alas......" sighed lightly, and Chen Zhou finally stopped writing.

I only habitually hold a pen and keep pointing on the scratch paper.

Yang Yiyi, who had been looking at Chen Zhou, asked softly, "Why do you sigh?"

Chen Zhou turned his head to look at Yang Yiyi in frustration: "It's fleeting, I didn't catch ......"

"Didn't catch it?"

"Well, it feels like it's almost ......"

Hearing Chen Zhou say this, Yang Yiyi also felt very sorry for Chen Zhou.

Especially just now, she also saw Chen Zhou's preoccupied and radiant appearance.

It's as if the answer is right in front of you.

After thinking about it, Yang Yiyi said: "It's good to catch it next time, I believe you." ”

Chen Zhou looked at Yang Yiyi's sincere eyes and nodded slightly.