Xueba starts with change

Chapter 274 Didn't catch it? (Happy Qixi Festival!)
The literature that caught Chen Zhou's eyes was another tool in the field of number theory research.

That is, the round method.

It and the sieve method 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 rate.

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

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

Of these three, none of Chen Zhou was unfamiliar.

Ramanujan, for his outstanding contributions in mathematics, so that in India, together with Mahatma Gandhi, the poet Rabindranath Tagore and others, he is called the "son of India".

Moreover, there are now two international mathematics awards named after Ramanujan.

Hardy and Littlewood, both British mathematicians, made outstanding research on Diophantine analysis, heap number theory, product number theory, and trigonometric series.

And they jointly completed a new proof of Waring's theorem.

Speaking of trigonometric series, Fourier series is a kind of trigonometric series.

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

With the help of Hardy, Ramanujan gradually emerged as a mathematician.

Speaking of Hardy.

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

The reason why Huaguo can achieve "1+2" ​​in number theory, or in Goldbach's conjecture, is Mr. Chen.

In fact, there is more or less a relationship with Hardy.

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

However, the method used by Mr. Chen to advance Goldbach's conjecture to "1+2" ​​is the weighted sieve method, not the circle method.

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

Then, they found that this thing seems to have some connection with Goldbach's conjecture.

So he perfected the theory of the round method, and gave a method, a method to describe the [There is a method of dismantling] in mathematical language.

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

【∫01e^(2πimα)dα】

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

When m≠0, the exponent cannot be 0. According to Euler's formula, the entire power becomes 0.

So the whole score is 0.

Using this property, the integral can be transformed into a function of the split method.

每一个N=p1+p2，p1，p2≥3的拆法就可以写成D(N)=∫01(2＜p≤N∑e^(2πiαp)^2)e^(2πiα(-N))dα。

同理，N=p1+p2+p3，p1，p2，p3≥3的拆法就可以写成T(N)=∫01(2＜p≤N∑e^(2πiαp)^3)e^(2πiα(-N))dα。

In this way, the proof [always has the dismantling method] is to prove that for any N that satisfies the meaning of the question, there is always D(N)>0, and T(N)>0.

At this point, we can start discussing points.

This is the main idea of ​​[Yuanfa].

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

In simple terms, it is to analyze the function on the circumference.

In contrast, the sieve method, which is the front and back of a coin, aims to give an approximate estimate of the distribution of prime numbers.

"Since the sieving method may not work, then try the round method..."

Chen Zhou was thinking in his heart, but he was not in a hurry with the movements of his hands.

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

If a workman wants to be good, he must first sharpen his weapon.

Chen Zhou has not fully understood the application of the round method.

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

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

Staring closely 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 tricks in the field of number theory.

For example, the generalized Riemann hypothesis can be used to prove some limited special cases.

Then use these special cases to prove something else.

Like the so-called "zero-free zone".

Although I don't know how to prove that the real part of all non-trivial zeros is 1/2.

But it has been proved that the zero point must be in a region containing the so-called "critical line", and this region is very small near the real axis.

Since then, people have been using similar conclusions to prove other issues.

However, Chen Zhou didn't like this method very much.

Because it is a bit strange to use an unproved conjecture to solve another conjecture.

What if the Riemann Hypothesis is falsified?
Even if this probability is very small, even if thousands of mathematical problems have been solved by relying on the Riemann Hypothesis, Chen Zhou is still unwilling to try.

He still hopes to step on every step firmly.

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

That's another matter.

Time moved forward slowly, and after Chen Zhou had read several documents, he turned to actual combat.

Yang Yiyi on the side looked curiously at what Chen Zhou had written on the draft paper.

However, she read it once, but she didn't understand it very well.

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

This situation is a bit familiar...

How should I put it, like...

Just like the feeling when Chen Zhou quickly solved the hail conjecture last time.

Could it be that?
Yang Yiyi, who was thinking like this, had a hint of surprise in her eyes.

She remembered that she heard Chen Zhou say last time that what he was studying was Kramer's conjecture. This seems to be a mathematical problem that has plagued the mathematics world for nearly a hundred years, right?

Is it going to be resolved so soon?
Yang Yiyi just looked at Chen Zhou like this, feeling a little lost for a moment.

Chen Zhou is studying with all his heart, how to use the round method to solve the correction problem of Kramer's conjecture.

When reading the literature, for a moment, he felt that he had caught the fleeting inspiration.

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

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

He also had no success with this fix.

Gradually, the speed at which the pen in Chen Zhou's hand was rubbing against the draft paper slowed down.

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

His brows were already furrowed unconsciously.

"Ah..." Sighing lightly, Chen Zhou finally stopped writing.

I just habitually hold a pen and keep lighting on the draft paper.

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

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

"Didn't catch it?"

"Well, it feels a bit close..."

Hearing what Chen Zhou said, Yang Yiyi also felt very sorry for Chen Zhou.

Especially just now, she saw Chen Zhou's concentration and high spirits.

As if the answer was right in front of us.

After thinking about it, Yang Yiyi said: "Just catch it next time, I believe in you."

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

(End of this chapter)