Chapter 255

"This formula, this formula ......"

Gu Lu seemed to have thought of something, and kept muttering these four words in his mouth.

Bao Zi next to him noticed Gu Lu's abnormality, tilted his head, and stared at Gu Lu with a look full of doubts.

It's just that Bao Zi didn't make a sound to wake Gu Lu up from this state.

It took dozens of seconds for Gu Lu to come back to his senses from this state.

Seeing Bao Zi with a puzzled face, Gu Lu handed the scratch paper in his hand to Bao Zi, "The solution to the problem you said is on this piece of paper, you should almost understand everything, as for what needs to be done later, you must understand without me saying it." ”

Bao Zi nodded.

After Gu Lu's guidance just now, Bao Zi was already full of confidence in overcoming the problems in front of him.

"Teacher, you just ......"

"Oh, nothing. Gu Lu smiled faintly.

It's nothing, it's just that a flash of inspiration flashed in his mind just now, and Gu Lu just happened to catch it.

"I won't mind if I borrow your desk to verify something, right?" Gu Lu said with a smile.

Bao Zi shook his head with a smile, then finished the last bun in three or two bites, sat opposite Gu Lu, and continued the work of the research group.

After Gu Lu's guidance, Bao Zi had a general idea of how to solve the current problems.

The atmosphere in the office instantly became quiet.

Except for the whirring wind outside, all that remained was the rustle of the tips of the two pens rubbing against the paper.

…………

“…… According to the formula S(x): =∑(1≤m1,m2,m3≤x)d(m1^2+m2^2+m3^2)=8ζ(3)/5ζ(4)x^3logx+O(x^3), simple improvements can be made. ”

After improvement, we get a formula like this, S(x)=2C1I1x^3logx+(C1I2+C2I1)x^3+O(x^(8/3+e). ”

Gu Lu's eyes were firmly fixed on the formula he had written, and the corners of his mouth gradually raised a trace of arc.

His guess was correct!

After a certain number of derivation and formula transformation, it may be possible to obtain a formula for the distribution of integer primes in the sphere.

And this formula is the answer to the problem of the whole point in the ball!

Gu Lu's expression was a little excited.

It's just a normal instruction.

But who would have thought that by chance, he would encounter the opportunity to solve the whole problem in the ball in one fell swoop.

When guiding Bao Zi just now, when Gu Lu saw the whole picture of the formula he finally derived, he faintly had that feeling.

It was as if he had discovered something terrible.

Because that formula, as long as it is slightly deformed, is structurally very similar to an important formula in the set of theories proposed by a certain mathematician in the last century in his attempt to solve the spherical whole point problem.

But the difference between the two is that.

The formula in front of me is much more perfect than that of the mathematician.

One of the main reasons why the mathematician did not succeed in solving the whole point problem in the sphere was that the formula was not perfect.

Gu Lu realized that maybe he could use this mean formula of the divisor function obtained by chance to try to attack the whole point problem in the ball!

Gu Lu's brain was running at high speed.

The intraspherical point problem is a problem that can be solved purely by mutual derivation between formulas.

To put it simply, Equation 2 is obtained from Equation 1, and then Equation 3 is obtained by Equation 1 or the combination of Equation 1 and 2, and so on.

In the end, it may take dozens of formulas before you get the final formula you need.

As a result, the final content on paper may be only a few pages.

But its cumbersomeness is definitely no less than a dozen or even dozens of pages of paper.

And it's a test of inspiration.

Inspiration is bursting, and it may be smooth sailing.

If you run out of inspiration, you can't move an inch.

And Gu Lu is completely in a state of inspiration today.

Starting from the most basic formula 1, Gu Lu gradually deduced it, and in less than half an hour, it was deduced to formula 10.

This is getting closer and closer to the formula that Gu Lu wants.

Gu Lu took advantage of the situation to pursue, and one formula after another jumped on the paper under Gu Lu's pen.

Gu Lu's attention was highly concentrated, and there was nothing else in his eyes except for this dense formula.

Now Gu Lu seems to have entered a state of self-forgetfulness.

…………

So, when Luo Yu walked into the office at eight o'clock in the morning, what he saw was a scene of Gu Lu and Bao Zi sitting opposite each other, silent.

Luo Yu walked over to this side suspiciously, stood behind Gu Lu, and frowned at the dense and complicated formula that Gu Lu had written on the paper.

Luo Yu is a Ph.D. majoring in number theory, so most of the formulas written by Gu Lu on the paper can be read by Luo Yu.

It's just that it takes some time to understand.

"It's ......"

Luo Yu vaguely saw that Gu Lu was looking for a certain question about the distribution of prime numbers.

But which one it is, Luo Yu can't say yet.

Instead of choosing to go to the desk to continue today's research work, Luo Yu just stood behind Gu Lu and carefully read these formulas written on paper by Gu Lu step by step from beginning to end.

Luo Yu just reads, while Gu Lu derives step by step from nothing.

But all the time, Luo Yu's speed of watching has never caught up with the speed of Gu Lu's writing.

However, as time passed, Luo Yu finally understood what Gu Lu was solving.

Ball Hour Problem!

Luo Yu is no stranger to this problem.

As far as he knew, the intrasphere point problem was a problem in the field of analytic number theory that existed in the last century.

Many mathematicians, both at home and abroad, have attacked it.

In fact, even Academician Chen, the current vice president of the Chinese Mathematical Society, spent a lot of effort on the whole point of the ball when he was young.

Although Academician Chen has made many research achievements and major breakthroughs in the direction of the ball point problem, after all, the ball point point problem has not been completely solved.

And now, Luo Yu saw with his own eyes that the young teacher in front of him was attacking the whole problem in the ball.

"Will it work?"

Luo Yu didn't know.

In fact, Luo Yu didn't believe that Gu Lu could solve the whole problem in the ball, but vaguely, Luo Yu chose to believe in Gu Lu.

Gu Lu lowered his head and wrote without distraction, not noticing Luo Yu standing behind him at all.

Near, closer......

When the twentieth formula was derived, Gu Lu realized that he was only a few steps away from the real answer.

Gu Lu's breath became short.

“…… From Equation 12, Equation 17, Equation 20, Equation 21 is: ∑(1≤m1,m2≤x)d(m1^2+m2^2)=A1x^2logx+A2x^2+O(x3/2+e)."

“…… Equation 22 can be obtained from Equation 3, Equation 14 and Equation 21 as: ......"

“…… From Equation 11 and Equation 22, Equation 23 is: π3(x): =∑(m1^2+m2^2+m3^2=p≤x)1~4π/3*x^1.5/logx."

Gu Lu wrote down the prime number distribution formula that represents the answer to the whole point problem in the sphere on the paper one by one.

"From Equation 2 and Equation 23, the prime distribution formula for the whole point in the sphere is: ∑(m1^2+m2^2+m3^2≤x)1=4π/3*x^1.5+O(x^2/3)!"

The whole problem in the ball, done!