Scholar’s Advanced Technological System

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

Although the plan of the mass projector is on the work schedule of the Lunar Orbital Construction Committee, I still don't know when I want to build this thing.

During this time, he could do something else first.

Anyway, the projects on the moon depend on the on-hook. Will there be tasks running there? At most, they will be postponed for a while to complete.

[Golden Reward Mission On! 】

[Explanation: The throne of the old era has stood for a century and a half. The beginning of the new era is bound to be the prelude to the end of the old era! The first step to the future, starting with mathematics ...]

[Requirement: Prove Riemann's conjecture within three years! 】

[Quest reward: 10,000 points, two million mathematical experience, a "legend" mission card. 】

"... Did you prove Riemann's conjecture within three years?"

Looking at the contents of the holographic panel from beginning to end, Lu Zhou thought to himself thoughtfully.

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

"Maybe look down on me too much."

At last, he confirmed the task description and requirements, Lu Zhou smiled slightly, and swiped his forefinger gently on the holographic screen to close the updated task bar.

It is not easy to prove the Riemann conjecture. Even if the Riemann conjecture is proved, it just opens a road to the top of the mountain. It takes a lot of effort to reach the top of the mountain.

But even then?

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 not only a mathematical intuition, but also the self-confidence brought by Lien Chan in the field of mathematics for a long time!

"The" Legend "mission card is really exciting ..."

Since they are all called legends, they should be more advanced than gold mission cards.

Although I don't know what is hidden on the back of that card, but the thought of defining it is the word legend, and Lu Zhou's heart was full of emotions ...

...

After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and recovered from closing his eyes.

The familiar warm current gradually climbed into the brain along the spine, and with the feeling of being immersed in the hot spring spreading to the limbs along the neural network, Lu Zhou felt that his spirit had never been higher and his civic field had never been clearer.

It feels like ...

One step closer to the omniscient God.

It didn't take long to transform the brain, and the warm current that climbed up the spine was completely scattered.

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

Gaze at the only person in the office, and saw the little girl's face turn red gradually, stuttering.

"... I think you slept well, so I put it on for you."

Looking at Han Mengqi who was explaining in a hurry, Lu Zhou said with a smile.

"Thank you."

"You're welcome ... that, you set my question, I've done it."

The steam on his forehead was about to emit steam, and Han Mengqi strayed away from the line of sight with Lu Zhou, stepped on the small broken steps, and handed out the stack of A4 paper that was almost full.

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

"let me see."

Not much nonsense, Lu Zhou took the stack of A4 paper from the little girl's hand, and glanced roughly.

The line at the head of the article was the title he assigned her last month.

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

Looking down, it took about 5 minutes. Lu Zhou looked at the calculation process of five or six pages from the beginning to the end, and then gave a relatively fair evaluation.

"Very standard proof."

Looking away from the proof process in his hand, Lu Zhou glanced at the calendar, and then returned the proof process to Han Mengqi, who was waiting for the result.

"Surprisingly, I thought you would take more time to prove it. I didn't expect you to finish it this year."

Hearing the compliment, the pressed corner of the lips couldn't help raising a touch of pride, Han Mengqi snorted softly.

"... I'm very smart."

Lu Zhou smiled slightly.

"I will personally confirm this."

Looking at Lu Zhou who was preparing to ask questions, Han Mengqi struck a hundred and twenty spirits, and said with eagerness.

"You ask!"

"Page three, line 16."

The sound of flipping paper sounded, and Han Mengqi quickly found the location of the line.

Holding up the slightly cool coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to introduce ζ (2n) from Equation 2 as a transcendental number."

Hearing this question, Han Mengqi's heart was relieved.

Before she came, she was ready to make things difficult for Lu Zhou. I did not expect that Lu Zhou didn't make things difficult for her, but asked a very basic one.

Taking a deep breath, she paused for a moment before continuing.

"... It can be obtained by transforming Equation 2 according to Euler's formula. For any integer n> 1, ζ (2n) = b (n) π ^ (2n)."

"Where b (2n) is a sequence of rational numbers, that is, Bernoulli numbers. Obviously ζ (2) is π ^ 2 times a special rational number, and ζ (4) is π ^ 4 times 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, of course, these function values ​​are also transcendental numbers. "

After listening to Han Mengqi's statement, Lu Zhou nodded approvingly.

"Good."

"But don't rush into pride. This question is only a test of whether you have completed this thesis yourself. The next question is the real challenge."

Looking at Han Mengqi, who was waiting in a tight array, Lu Zhou put down the coffee cup in his hand and continued to ask.

"Now that you have proven that ζ (2n) is a transcendental number, what I want to ask is, what about ζ (3)?"

Such a simple question ...

Han Mengqi raised her chin proudly.

But just as she was about to answer the question, she froze.

ζ (3)!

ζ (3) ...

Huh?

What exactly is this thing? !!

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

"Can't answer it? Ζ (3) seems simpler than ζ (2n), right? The latter has an unknown in parentheses."

"Hmm ..." The cheek gangster bulged, and Han Mengqi, biting her lower lip, thought hard, but couldn't say a word.

After a while, he asked tentatively.

"Also ... beyond numbers?"

Lu Zhou asked with a smile: "Oh? Why?"

Han Mengqi answered honestly: "... guess."

Seeing the little girl's head lowered honestly, Lu Zhou smiled, paused for a moment and continued.

"It is not surprising that you don't know, because Euler who wrote the Euler formula does not know. It was not until 1978 that the French mathematician y proved that ζ (3) was not a rational number, and whether ζ (5) was a rational number, we Don't know yet. "

When Lu Zhou asked his own question, there was no answer at all, Han Mengqi said suddenly.

"Why ... take this unanswered question ... bully me ~ www.readwn.com ~ there are answers," looking at Han Mengqi, Lu Zhou smiled, and said in a serious tone, "Any math problem has an answer, but we don't know it yet. When you graduate from a master's to a PhD, the challenge is here, you have to learn to find a way to the exit of the maze and propose Idea, and then make it happen. "

After hearing Lu Zhou's words, Han Mengqi gave a little sting.

Immediately she responded with a surprise expression on her face.

"Wait, wait, you mean, decided to take me as a disciple ?!"

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."

Speaking, Lu Zhou got up from the back of his desk, walked to the blackboard in the office, picked up a piece of chalk, and wrote on the blackboard while talking.

"The transcendental value of the Riemann zeta function at odd positive integer points has always been a classic problem in analytical mathematical theory. According to Euler's formula and the properties of Bernoulli numbers, it can be easily proved that ζ (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 so far is that there are countless multiple ζ (2n + 1) as irrational numbers, but the mathematical difference between infinity and infinity is also so far away from infinity."

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

"By then, you will be able to graduate from me."

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