Chapter 846 Three Years!

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

Although the plan for the mass catapult is on the work schedule of the Lunar Orbit Construction Committee, it is still unclear when it will be completed.

During this time, he can do something else first.

Anyway, the projects on the moon depend on hanging up the phone, and the task will not run away there, at most it will be delayed a little later to complete it.

[Golden reward mission is open! 】

[Explanation: The throne of the old era has been standing for a century and a half, and the beginning of the new era will surely be preceded by the end of the old era! The first step on the road to the future starts with mathematics...]

[Requirement: Solve the Riemann Hypothesis within three years! 】

[Mission rewards: 10,000 points, 2 million math experience, and a "Legend" mission card. 】

"... Will the Riemann Hypothesis be solved within three years?"

Lu Zhou saw the content on the holographic panel from beginning to end expressionlessly, and said to himself thoughtfully.

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

"You must have underestimated me."

Finally, after confirming the mission description and requirements, Lu Zhou smiled lightly, and gently swiped his index finger across the holographic screen to close the updated mission bar.

It is not an easy task to prove the Riemann Hypothesis. Even if the Quasi-Riemann Hypothesis is proved, it only opens an intersection leading to the top of the mountain, and it will take a lot of effort to reach the top of the mountain.

But so what?

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

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

This is not only a kind of mathematical intuition, but also the confidence brought by his continuous victories 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 higher-level existences than the golden mission cards.

Although he didn't know what was hidden on the back of the card, but when he thought that it was defined by the word legend, Lu Zhou's heart surged...

...

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

The familiar warm current gradually climbed up the brain along the spine, and as a feeling of soaking in the hot spring spread to the limbs along the nerve network, Lu Zhou felt his spirit was unprecedentedly high, and his Civic was unprecedentedly clear.

It feels like...

One step closer to the all-knowing and all-powerful God.

It didn't take too long for the transformation of the brain area, and the warm current that climbed up the spine dissipated completely in an instant.

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

I met the only person in the office, and saw that the little girl's face gradually turned red, and she stammered.

"...I see that you are sleeping soundly, so I will put it on for you."

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

"thanks."

"You're welcome... Well, you set my question, I have already done it."

Her forehead was so hot that it was about to emit steam. Han Mengqi lost her sight of Lu Zhou, stepped forward with small steps, and handed out the almost full stack of A4 papers in her hand with a look of anxiety.

"I don't know if it's right, but... I figured it out myself."

"let me see."

Without much nonsense, Lu Zhou took the stack of A4 papers from the little girl's hands and glanced at them roughly.

The line at the top of the article is the topic 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. 】

Keeping his gaze down, it took about 5 minutes for Lu Zhou to read the five or six pages of calculation process from beginning to end, and then gave a more pertinent evaluation.

"Pretty standard method of proof."

Taking his eyes off the proof process in his hand, Lu Zhou glanced at the calendar, and then returned the proof process to Han Mengqi who was anxiously waiting for the result.

"Surprisingly, I thought you would spend more time to prove it, but I didn't expect you to complete it this year."

Hearing this praise, the corners of her pressed lips couldn't help but twitched with pride, Han Mengqi snorted softly and said.

"...I'm very smart."

Lu Zhou smiled lightly.

"I will confirm this myself."

Looking at Lu Zhou who was about to ask questions, Han Mengqi cheered up and said in a prepared manner.

"Ask!"

"Page 3, line 16."

The sound of flipping paper was heard, and Han Mengqi quickly found the location of that row.

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

Hearing this question, Han Mengqi secretly heaved a sigh of relief.

Before coming here, she was already prepared to be made things difficult by Lu Zhou. Unexpectedly, Lu Zhou didn't make things difficult for her with such a particularly difficult question, but just asked a very basic one.

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

"...According to Euler's formula, the formula 2 can be transformed. For any integer n>1, there is ζ(2n)=b(n)π^(2n)."

"where b(2n) is a sequence of rational numbers, the Bernoulli numbers. It is obvious that ζ(2) is π^2 multiplied by a particular rational number, and ζ(4) is π^4 multiplied by a particular rational number...so we It is completely clear that ζ(2), ζ(4)...are all rational numbers. And because π is a transcendental number, these function values ​​are of course also a transcendental number.”

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

"good."

"But don't rush to be proud. This question is just to test whether you have completed this thesis yourself. The next question is the real challenge."

Looking at Han Mengqi who was waiting in full battle, 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, what I want to ask is, what about ζ(3)?"

Such a simple question...

Han Mengqi raised her chin triumphantly.

However, just when she was about to answer this question, she was stunned.

ζ(3)!

ζ(3)...

Huh huh?

What the hell is this thing? !

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

"I can't answer it? ζ(3) seems simpler than ζ(2n), right? The latter still has an unknown number in the brackets."

"Hmm..." Her cheeks bulged, and Han Mengqi bit her lower lip, thinking hard, but she couldn't say a word.

After a while, he asked in a tentative tone.

"It's also... a transcendent number?"

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

Han Mengqi replied honestly: "... guessed."

Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.

"It's not surprising that you don't know, because Euler who wrote Euler's formula didn't know either. It wasn't until 1978 that the French mathematician R. Apery proved that ζ(3) is not a rational number, and whether ζ(5) is a rational number , we don’t know yet.”

Hearing that there was no answer to Lu Zhou's question, Han Mengqi said angrily.

"What... use this kind of question that has no answer... to bully me."

"There is an answer," Lu Zhou looked at Han Mengqi, smiled, and then said in a serious tone, "Any mathematical question has an answer, but we don't know it yet. And when you become a doctor from a master Afterwards, the challenges you face are right here, you have to learn to find a way to the exit of the maze by yourself, come up with Ideas, and then realize them.”

After hearing Lu Zhou's words, Han Mengqi was slightly taken aback.

Then she reacted suddenly, with a surprised expression on her face.

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

Lu Zhou smiled and nodded.

"After you successfully answered the first question, I have actually made up my mind."

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

After speaking, Lu Zhou stood up from behind the desk, walked to the blackboard in the office, picked up a half-used chalk, and wrote on the blackboard while talking.

"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 properties of Bernoulli numbers, it can be easily proved that ζ(2n) is a transcendental number, Therefore people conjecture that for any integer n>1, ζ(2n+1) is also a transcendental number.”

"The best result so far is that there are infinitely many ζ(2n+1) that are irrational numbers, but the difference between infinity and infinity in mathematics is as far 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 an achievement recognized by the academic community."

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