Scholar’s Advanced Technological System

Looking at the unfolding taskbar for about five minutes, Lu Zhou finally chose to use the reward task card.

The plan of the quality projector is on the work schedule of the Lunar Track Construction Committee, but I don’t know when to go when I want to build this stuff.

During this time, he can do something else first.

Anyway, the project on the moon depends on the hang-up, and the task can not be run there, at most, it is only postponed a little later to complete.

[Gold reward mission is open! 】

[Description: The throne of the old era has stood for one and a half centuries, and the start of the new era will surely follow the end of the old era! The first step to the road to the future begins with mathematics...]

[Requirement: Prove the Riemann conjecture within three years! 】

[Task reward: 10,000 points, 2 million math experience, a "legend" mission card. 】

"...Is Riemann guessing within three years?"

Facelessly, the contents of the holographic panel were seen from the beginning, and Lu Zhou thought to himself.

"Although this is the top crown in mathematics, but three years..."

"It’s too small to look at me too."

Finally, I confirmed the task description and requirements. Lu Zhou smiled lightly. The index finger gently crossed the holographic screen and turned off the updated taskbar.

It is not an easy task to prove the Riemann conjecture. Even if it proves the Quasi-Riemann conjecture, it is just opening a junction to the top of the mountain. It takes a lot of effort to get to the top of the mountain.

But what about it?

There has never been a problem that can bother him for three years...

Lu Zhou has no doubt that he can solve this problem within three years.

This is both a mathematical intuition and a confidence that he has brought to the Lien Chan in the field of mathematics for a long time!

"The 'legend' mission card is really exciting..."

Since they are called legends, then it should be more advanced than the Golden Mission Card.

Although I don’t know what the back of the card is hiding, but when I think of the word that defines it, Lu Zhou’s heart is full of enthusiasm...

......

After leaving the system space, the boat in the office slowly opened his eyes and returned from the closed eyes.

The familiar warmth gradually climbed up the brain along the spine. As the feeling of being soaked in the hot spring spread along the neural network to the limbs, Lu Zhou felt that his spirit had never been higher than ever before, and the Civic was unprecedentedly clear.

This feeling is like...

A step closer to the omniscient God.

The transformation of the brain domain did not take too long, and the warm current that climbed the spine was scattered.

Gently moving the shoulder and feeling the weight on the shoulder, Lu Zhou reached out and touched it and found that his shoulder was covered with a blanket.

The only person in the office looked up and saw the little girl's face gradually reddening and stuttering.

"...I see you are very fragrant, just help you."

Looking at Han Mengqi who was hurriedly explained, Lu Zhou smiled and said.

"Thank you."

"You're welcome...that, you have arranged my problem, I have already finished."

The forehead was hot and steamed. Han Mengqi was at a loss and staggered the line of sight with Lu Zhou. He stepped on the small piece and stepped forward, and he handed out the stack of almost a4 paper.

"I don't know if it's right, but... I thought about it myself."

"let me see."

No more nonsense, Lu Zhou took the stack of a4 paper from the girl's hand and roughly glanced at it.

The line at the top of the article is the one he had assigned to her last month.

[For any real number s>1, define ζ(s)=Σ1/(m^s), and verify that ζ(2n) is the transcendental number. 】

The line of sight continued to go down. It took about 5 minutes. Lu Zhou saw the full five or six pages of calculation process from the beginning, and then gave a more pertinent evaluation.

"A very standard proof method."

The line of sight left the proof process in the hand, Lu Zhou looked at the calendar, and then returned the proof process to Han Mengqi, who was waiting for the result.

"It's amazing, I thought you would spend more time to prove it. I didn't expect you to finish this year."

Hearing this praise, the pressed lips couldn't help but sway a little, and Han Mengqi snorted softly.

"...I am very smart."

Lu Zhou smiled lightly.

"I will confirm this on my own."

Looking at Lu Zhou, who is ready to ask questions, Han Mengqi played the spirit of one hundred and twenty cents, and he said that he was waiting.

"You ask!"

"The third page is line 16."

When the paper was squeaking, Han Mengqi quickly found the position of the line.

Picking up the slightly cool coffee cup on the table and gently taking a sip, Lu Zhou paused for a while and continued: "Detailed instructions on how to push ζ (2n) from the type 2 to exceed the number."

Hearing this question, Han Mengqi’s heart was secretly relieved.

Before she came, she had already prepared for being difficult by Lu Zhou. I did not expect that Lu Zhou did not take the particularly difficult problem to marry her. She just asked a very basic one.

Taking a deep breath, she paused for a moment and continued.

"... According to Euler's formula, we can get the formula 2, for any integer n>1, we have ζ(2n)=b(n)π^(2n)."

"where b(2n) is a sequence of rational numbers, ie bernoulli numbers. Obviously ζ(2) is π^2 multiplied by a special rational number, ζ(4) is π^4 multiplied by a special rational number...so we It is completely clear that ζ(2), ζ(4)... are rational numbers. And because π is a transcendental number, these function values ​​are of course also transcendental numbers."

After listening to Han Mengqi’s statement, Lu Zhou applauded and nodded.

"Not bad."

"But don't be eager to be proud. This question is only to test whether your paper is completed by yourself. The next question is the real challenge."

Looking at the stern waiting for Han Mengqi, Lu Zhou put down the coffee cup in his hand and continued to ask.

"Since you have proved that ζ(2n) is a transcendental number, then what I want to ask is, ζ(3)?"

Such a simple question...

Han Mengqi proudly lifted his chin.

However, just as she was preparing to answer this question, she was stunned.

ζ (3)!

ζ(3)......

Hey?

What is this stuff? !

Looking at the face of Han Mengqi, Lu Zhou asked with a smile.

"Isn't the answer? ζ(3) It seems to be simpler than ζ(2n)? The latter has an unknown number in brackets."

"Oh..." The gang swelled up, Han Mengqi biting his lower lip, thinking hard, but he couldn't say a word.

After a while, I asked with a tentative tone.

"Also... beyond?"

Lu Zhou smiled and asked: "Oh? Why?"

Han Mengqi honestly replied: "... guess."

Looking at the little girl's honestly looking down, Lu Zhou smiled and paused for a moment to continue.

"You don't know it is not strange, because Euler who wrote the Euler formula does not know. Until 1978, the French mathematician r.ap?ery proved that ζ(3) is not rational, but about ζ(5) is It’s not reasonable, we don’t know it now.”

When I heard Lu Zhou ask my own question, there was no answer at all. Han Mengqi said with enthusiasm.

"What?...take this unanswered question...to bully me."

"There are answers," looked at Han Mengqi. After Lu Zhou smiled, he changed into a serious tone and said, "Any math problem has an answer, but we don't know it. And when you become a doctor from master's degree. After that, the challenge is also here, you have to learn to find a way to the labyrinth exit, propose an idea, and then implement it."

After hearing the words of Lu Zhou, Han Mengqi first stunned.

Then she replied violently, and a surprise expression appeared on her face.

"Wait, wait a minute, what do you mean, decided to accept me as a singer?!"

Lu Zhou smiled and nodded.

"After you successfully answered the first question, I actually decided."

"As for the second question, it is your research topic."

Said, Lu Zhou stood up from behind the desk, went to the blackboard in front of the office, picked up a piece of chalk, and wrote it on the blackboard, while talking.

"The transcendence of the value of the Riemann zeta function at odd integer points has always been a classic problem in the field of analytical numbers. According to Euler's formula and the nature of Bernoulli numbers, it is easy to prove that (2n) is a transcendental number. So people guess that for any integer n>1, ζ(2n+1) is also a transcendental number."

"The best result at the moment is that there are countless numbers of ζ(2n+1) as irrational numbers, but the difference between infinity and infinity in mathematics is also so far from infinity."

"If you can move forward in this direction, even if it is only a small step, as long as it is enough to be recognized by the academic community."

"At that time, you will be able to graduate from me."