Lu Zhou looked at the mission panel and pondered for about five minutes. In the end, he chose to use the mission reward card.
Even though the mass launcher was on the Lunar Orbit Committee's agenda, they didn't know how long it would take to build it.
During this time, he could do something else first.
Anyway, the construction on the Moon depended on the AFK, so the mission wouldn't run away. At most, it would just be delayed a bit.
[Gold reward mission activated!]
[Description: The throne of the old era has stood for a century and a half. The start of the new era will inevitably end with the end of the old era! The first step on the road to the future begins with mathematics …]
[Requirements: Prove Riemann's conjecture within three years!]
[Mission reward: 10,000 general points, two million mathematics experience points, a "legendary" mission card.]
"… Prove Riemann's conjecture within three years?"
Lu Zhou read the contents on the holographic panel from beginning to end with a blank expression. He spoke to himself thoughtfully.
He muttered to himself, "Even though this is the crown of mathematics, three years …"
"You're underestimating me."
Lu Zhou looked at the mission description and requirements one last time. He smiled and gently swiped his index finger across the holographic screen. He closed the updated mission panel.
Proving Riemann's conjecture was not an easy task. Even if he proved the quasi- Riemann's conjecture, it would only open up a path to the top of the mountain. It would take a lot of effort to climb to the top.
But even so, so what?
There had never been a problem that bothered him for three years …
Lu Zhou had no doubt that he could solve this problem within three years.
This was both a mathematical intuition and the confidence that came from his years of experience in the field of mathematics!
"A" legendary "mission card, I'm really looking forward to it …"
Since it's called a legendary mission card, it should be something higher than a golden mission card.
Even though Lu Zhou didn't know what was hidden on the back of the card, he couldn't help but feel excited when he thought about the word "legendary" …
…
After leaving the System Space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses.
The familiar warm current gradually climbed up his spine to his brain. As the feeling of being soaked in a hot spring spread along the neural network to his limbs, Lu Zhou felt that his spirit was unprecedentedly high, and his thoughts were unprecedentedly clear.
This feeling was just like …
He was one step closer to the omniscient and omnipotent God.
The modification of the brain didn't take too long, and the warm feeling that climbed up his spine disappeared in an instant.
Gently moving his shoulders, Lu Zhou felt the weight on his shoulders. He reached out and found that his shoulders were covered with a blanket.
She made eye contact with the only person in the office. The little girl's face gradually turned red as she stammered.
"… I saw that you were sleeping soundly, so, so I put it on for you."
Looking at Han Mengqi who was hurriedly explaining, Lu Zhou smiled and said.
"Thank you."
"You're welcome … Um, I've finished the problem you asked me."
Han Mengqi's forehead was so hot that it was about to emit steam. She didn't know what to do when she looked at Lu Zhou. She walked forward and handed over the stack of A4 papers in her hand.
"I don't know if it's correct, but … I figured it out myself."
"Let me see."
Without wasting any time, Lu Zhou took the stack of A4 papers from the little girl's hand and glanced at it.
The line at the beginning of the article was the problem he assigned to her last month.
[For any real number s > 1, define ζ (s) = Σ1/(m ^ s), and prove that ζ (2n) is a transcendental number.]
Lu Zhou continued to read, and it took him about five minutes to read the five or six pages of calculations from beginning to end. He then gave a more pertinent evaluation.
"A very standard proof method."
Lu Zhou looked at the calendar and returned the proof process to Han Mengqi, who was waiting for the result with a nervous look on her face.
"Amazing, I thought you would take more time to prove it, I didn't expect you to finish it this year."
Hearing this praise, Han Mengqi's lips couldn't help but curl up into a proud smile. She lightly snorted and said.
"… I'm very smart."
Lu Zhou smiled faintly.
"I'll confirm this myself."
Han Mengqi looked at Lu Zhou, who was about to ask a question. She focused her attention and spoke.
"Go ahead!"
"Page three, line 16."
With the sound of paper flipping, Han Mengqi quickly found the position of the line.
Lu Zhou picked up the slightly cold coffee cup on the table and took a sip. He paused for a moment and continued, "Explain in detail how to deduce ζ (2n) from formula 2 to be a transcendental number."
When Han Mengqi heard this question, she secretly breathed a sigh of relief.
Before she came here, she was prepared to be troubled by Lu Zhou. She didn't expect Lu Zhou to only ask a very basic question.
She took a deep breath and paused for a moment before continuing.
"According to Euler's formula, we can get that for any integer n > 1, ζ (2n) = b (n) π ^ (2n).
"Where b (2n) is a sequence of rational numbers, that is, the Bernoulli number. Obviously, ζ (2) is π ^ 2 times a special rational number, and ζ (4) is π ^ 4 times a special rational number … So we are completely clear that ζ (2), ζ (4) … are all rational numbers. Because π is a transcendental number, these function values are of course also transcendental numbers. "
After listening to Han Mengqi's statement, Lu Zhou nodded with approval.
"Not bad.
"But don't be too proud. This question is just to test whether you wrote this paper by yourself. The next question is the real challenge. "
Lu Zhou looked at Han Mengqi and put down the coffee cup in his hand.
"Since you already proved that ζ (2n) is a transcendental number, then I want to ask, what about ζ (3)?"
Such a simple question …
Han Mengqi proudly raised her chin.
However, when she was about to answer this question, she froze.
Ζ (3)!
Ζ (3) …
Huh huh huh?
What the hell is this?!
Lu Zhou looked at the muddled Han Mengqi and smiled.
"You can't answer? Ζ (3) seems simpler than ζ (2n), right? The latter has an unknown number in parentheses. "
"Oh …" Han Mengqi's cheeks puffed up. She bit her lower lip and thought hard, but she couldn't say a word.
After a while, she asked in a tentative tone.
"Also … a transcendental number?"
Lu Zhou smiled and said, "Oh? Why? "
Han Mengqi answered honestly, "… I guessed."
Lu Zhou looked at the little girl's obedient look and smiled. He paused for a second before speaking.
"It's not surprising that you don't know, because Euler, who wrote the Euler formula, didn't know either. It wasn't until 1978 that the French mathematician Y. proved that ζ (3) is not a rational number. We still don't know whether ζ (5) is rational or not. "
When Han Mengqi heard that Lu Zhou didn't have an answer to her question, she suddenly spoke angrily.
"What the hell … Using this kind of question … to bully me."
"There is an answer." Lu Zhou looked at Han Mengqi and smiled. He then said in a serious tone, "Any mathematics problem has an answer, we just don't know it yet. When you become a PhD student, this is the challenge you face. You have to learn to find a way out of the maze, come up with an idea, and then implement it. "
After hearing Lu Zhou's words, Han Mengqi paused for a second.
Then, she suddenly reacted, and a look of surprise appeared on her face.
"Wait, wait a second, you're saying you've decided to accept me as your student?!"
Lu Zhou smiled and nodded.
"After you successfully answered the first question, I actually made up my mind.
"As for the second question, that's your research topic."
Lu Zhou stood up from behind his desk and walked to the blackboard in the office. He picked up a piece of chalk and wrote on the blackboard.
"The transcendence of the Riemann zeta function at odd positive integer points has always been a classic problem in the field of analytic number theory. According to Euler's formula and the nature of Bernoulli numbers, it is easy to prove that ζ (2n) is a transcendental number. Therefore, it is conjectured that for any integer n > 1, ζ (2n + 1) is also a transcendental number.
"The best result so far is that there are countless ζ (2n + 1) irrational numbers. However, the difference between infinity and infinity is as large as infinity.
"If you can take a step forward in this direction, even if it is only a small step, as long as it is recognized by the academic community.
"When that time comes, you will be able to graduate from me."
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