Chapter 845

Looking at the task bar, I thought about it for about five minutes. At last, Lu Zhou chose to use the reward task card.

Although the mass projector plan is on the agenda of the moon orbit construction committee, it is not known when it will be built.

During this time, he could do something else first.

Anyway, all the projects on the moon depend on hang ups. If the task is put there, it will not run. At most, it is only to postpone the completion of the task a little later.

[golden reward task open! ]

[Note: the throne of the old era has stood for a century and a half, and the start of the new era will be preceded by the end of the old era! For any real number s > 1, define ζ (s) = ∑ 1 / (m ^ s), and prove that ζ (2n) is transcendental. ]

it took about 5 minutes for the line of sight to go down. The ship saw the whole process from the beginning to the end, and then gave a more pertinent evaluation.

"Very standard method of proof."

The vision left the proving process in his hand, and Lu Zhou looked at the calendar, and then returned the proving process to Han Mengqi, who was waiting for the result anxiously.

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

Hearing the praise, the lips could not help lifting a trace of pride, Han Mengqi said softly.

“…… I'm very smart. "

The boat smiled faintly.

"I will personally confirm that."

Looking at Lu Zhou, who is ready to ask questions, Han Mengqi said with a spirit of 120 points.

"Ask!"

"Page three, line 16."

The sound of turning over the paper was heard, and Han Mengqi soon found the position of that line.

Take a sip of the cool coffee cup on the table, and the boat pauses for a moment, and continues, "explain in detail how to push ζ (2n) from formula 2 as the transcendental number."

Hearing this question, Han Mengqi felt relieved.

Before she came here, she was ready to be challenged by the land boat. Unexpectedly, the land boat did not challenge her with such a particularly difficult question, but asked a very basic one.

Taking a deep breath, she continued after a pause.

“…… According to the transformation of formula 2 by Euler formula, for any integer n > 1, there is ζ (2n) = B (n) π^ (2n). "

"Where B (2n) is a sequence of rational numbers, i.e. Bernoulli number. Obviously ζ (2) is π ^ 2 times a special rational number, ζ (4) is π ^ 4 times a special rational number So we know ζ (2), ζ (4) All are rational numbers. Because π is transcendental, of course, these function values are also transcendental. "

After hearing Han Mengqi's expression, Lu Zhou nodded approvingly.

"Not bad."

"But don't be too proud. The question is just to test whether you have finished this paper by yourself. The next question is the real challenge. "

Looking at Han Mengqi, who is waiting for Yan, Lu Zhou puts down his coffee cup and continues to ask.

"Since you have proved 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 was stunned.

ζ（3）！

ζ（3）……

Eh eh eh?

What is this thing?!

Looking at Han Mengqi's face, Lu Zhou asked with a smile.

"Can't answer? Is ζ (3) easier than ζ (2n)? There's an unknown number in the brackets

"Well..." Mumps puffed up, and Han Mengqi, who was biting her lower lip, thought bitterly, but could not say a word.

After a while, he asked in a tentative tone.

"Also Beyond number? "

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

Han Mengqi replied honestly: "I'm sorry Guess. "

Looking at the girl with her head down honestly, Lu Zhou smiled and paused for a moment to continue.

"It's not surprising that you don't know, because Euler, who wrote Euler's formula, doesn't know either. It wasn't until r.ap'ery, a French mathematician, proved in 1978 that ζ (3) was not a rational number, but we still don't know whether ζ (5) was a rational number. "

Hearing Lu Zhou's question, Han mengqiton said angrily.

"What Take this unanswered question Come and bully me. "

"There is an answer," Lu Zhou said in a serious tone after looking at Han Mengqi and laughing. "Any math problem has an answer, but we don't know it yet. And when you become a doctor from a master's degree, the challenge is also here. You have to learn to find a way to the exit of the maze, put forward idea, and then realize it. "After hearing Lu Zhou's words, Han Mengqi was slightly shocked.

Then she reacted with surprise.

"Wait, wait a minute, you mean, decided to take me as an apprentice?"

The boat smiled and nodded.

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

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

With that, Lu Zhou stood up from the back of the desk, went to the blackboard in the office, picked up a piece of chalk that was only half used, and wrote on the blackboard while talking.

"The transcendence of Riemannian zeta function at the point of odd positive integer has always been a classical problem in the field of analytic number theory. According to Euler formula and Bernoulli number, it is easy to prove that ζ (2n) is a transcendental number. Therefore, it is assumed that for any integer n > 1, ζ (2n + 1) is also a transcendental number. "

"At present, the best result is that there are countless ζ (2n + 1) irrational numbers, but the difference between infinity and infinity in mathematics is also as far away from infinity."

"If you can take a step forward in this direction, even if it's just a small step, as long as it's an achievement that's recognized by academia."

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