For the eight-poor mathematics community, any research on the Riemann conjecture will be talked about for a while.

This is no exception to the mathematics department of the University of Los Angeles at Berkeley on the West Coast.

As early as the preprint of Professor Lu’s paper, the first time to hang on arxiv, the quasi-Riemann conjecture was proved to be flying everywhere, just looking for a coffee shop to sit and hear someone excited. Discuss this difficult problem that has lasted for a century.

"Have you heard that? The Quasi-Riemann conjecture is proved!"

"I just heard that it is too unbelievable. No one has been able to translate the right side of the critical zone to the left for a century!"

"The last study on this direction led directly to the proof of the prime number theorem. I don't know what Professor Lu will bring to us this time."

"Hey, if I could have half of the IQ of Professor Lu, it would be fine."

"Wake up, don't dream!"

Not only are the students in the mathematics department at Berkeley, the professors are talking about this.

Although analytic number theory is not the strong direction of Berkeley, relatively speaking, it is more biased towards partial differential equations. However, for Tao Zexuan, a scholar who has few fields that are not proficient, naturally, he will not miss the big news in mathematics. .

The office of the mathematics department at Berkeley, sitting in front of a desk full of draft paper, and Tao Zhexuan, who turned a ballpoint pen in his hand, stared at the densely-written paper on the table, because it was too focused. As for the knocking on the door, I didn’t hear it.

The knock on the door continued to ring for a while, and the back door was pushed straight away. A tall, thin Asian man took a box of pizza and came in. From his skilled movements, it should be the doctor in this office.

"Professor, your pizza is here."

Without looking up, Tao Zhexuan said to him casually.

"Just put me aside."

"Okay, although I recommend you eat it hot," put the pizza on the table. The doctoral student glanced at the draft paper in front of the boss and curiously asked, "That, I saw it this morning. Your topic on mathoverflow... Are you still working on that paper?"

Tao Zhexuan: "Yes."

The throat was swallowed, and the doctoral student asked in the tone of expectation.

"Is there a result?"

"I will tell you if there is one."

"Okay." Listening to this cold voice, the doctoral student spit out his tongue and gave birth to a helpless expression and left the door.

Generally speaking, Professor Tao is relatively approachable, and among the many big cows at Berkeley, a few will be professors.

However, this is also an occasion.

Generally speaking, when he is troubled by any problem, even if his wife is coming, don't expect him to show how enthusiastic he is...

"interesting."

"The method of introducing algebraic geometry, in his paper, can see the shadow of Groentendik's work, but it is not particularly obvious."

"The key lies in the choice of algebraic curves on the complex plane... How did he come up with it?"

"And... can this method really be called proof?"

Leaning on the office chair and staring at the dusty ceiling fan at the top of the head, Tao Zhexuan scratched his head with some brains.

He rarely plagues things for so long.

The ballpoint pen gently clicked on the paper, and after sinking for a while, he spit out a word.

"there is controversy."

However, this sentence does not use a positive tone. When dealing with this problem, he is rarely able to be as confident as before.

"Is it wrong?"

Or is it really as he thinks, is there a problem?

......

Speaking of it, when was the last time I received an email from Vera, Lu Zhou had already remembered it.

Maybe a year ago?

Maybe it is a little longer.

Obviously, Vera, who is studying Riemann's conjecture, naturally sees the preprint he hangs on arxiv, and should have spent time researching it and having some questions.

A lot of things are difficult to discuss clearly in the mail. The two agreed to make a video call at 8:00 pm on the next day.

So...

After three years, Lu Zhou once again saw his most proud and most discouraged disciples.

Although there is a network cable...

At 8 o'clock the next night, the video call was opened.

Sitting in the study room with a cup of coffee, Lu Zhou was originally prepared to discuss academic issues, but the atmosphere was somewhat unexpectedly stiff.

It seems that I have a lot of words to talk about, and I don’t know how to speak. I just sit there nervously, staring at the computer screen and not talking.

And when Vera looked at the Lu Zhou in the video, she was also watching Vera's Lu Zhou. At this moment, the expression on her face was also subtle.

The golden hair is combed into a delicate princess, and the long skirt with silk edges outlines the curve of the shoulders. Even if the difference between the lipsticks can be seen, the boat can be seen. Obviously not a daily makeup, obviously dressed up.

What should I say at this time?

long time no see?

It seems a bit cold.

Your new hairstyle is very good?

Always feel that there will be unnecessary misunderstandings...

Gently coughed, Lu Zhou tried to make a formal expression and said with a clear voice.

"Go directly to the topic... let me see where your question is."

The chill and the guest will make the atmosphere a bit stiff. Everyone is engaged in mathematics and directly enters the topic. Maybe it will make the atmosphere a little easier.

Sure enough, with this sentence spoken, the atmosphere in the video call was slightly softer.

Vera, who was sitting at the end of the computer, also loosened her mouth, and then the chicken glutinous rice nodded like a nod, whispered.

"Hmm, please, please wait..."

Said, the little girl got up and walked to the side, and laboriously dragged a blackboard filled with heart from the side of the classroom.

Seeing the line of calculations on the blackboard, Lu Zhou squinted a little, and the eyes quickly flashed a trace of surprise, and then the expression gradually became serious.

Looking at Lu Zhou, who was in meditation, Vera cleared her throat and continued to whisper. "This is the algebraic geometry method you used to prove the Quasi-Riemann conjecture. I tried to summarize the method from the problem itself. ""

I quickly browsed the contents of the blackboard, and Lu Zhou nodded with approval and gave a positive evaluation.

"well done."

It is an apprentice he taught.

It is quite difficult to sort out these things.

Vera smiled embarrassedly: "Although Molina... Ms. Abel told me not to talk to you about these issues, I still think... it would be better to talk to you."

The idea of ​​communicating with genius is actually a risky thing, because the academic world only recognizes the results and does not recognize where the "idea" comes from.

So don't say that it's something that looks interesting. Sometimes even a staged result that is enough to get on the top of the magazine will be pressed by the author himself... if he has ambitions for higher goals, he doesn't belong to himself. The words of scholars who are indifferent to fame and fortune and do not care about the name.

After a pause, Vera put on a serious expression and continued.

"I have carefully studied the algebraic curve on the finite field that you introduced when proving that the e value is infinitely small, re(s) ≥ 1-e does not exist in the non-zero ordinary point of the ζ function, and according to ζ ( s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) properties are obtained..."

Said, Vera turned to face the blackboard, leaving a blank position at the corner, and wrote a line of calculations.

Looking at Vera's blackboard on the blackboard, Lu Zhou brows slightly, but soon there is slack.

He has a general understanding of Vera's ideas.

On the basis of her own proof method, she gives the planherel formula on a class of single-connected nilpotent lie groups by means of the mapping of homology groups. In short, she has improved his group structure. Then applied to the amplification of the e value.

The chalk that wandered on the blackboard gradually stopped, and Vera, who was coming back, smiled.

"It's probably workable by this method, but I can't do it in half. I think if it's you, you can find the reason..."

"So...it's fine if you can help you."

In the last sentence, Vera's voice is very small, so small that she is not sure, whether the land at the end of the video really heard.

Staring at the calculations on the blackboard, I looked at it for a while, and I stopped sitting there, and suddenly said.

"Do you know why you can't find the reason?"

Slightly squatted, Vera asked subconsciously.

"……why?"

With a regretful expression on his face, Lu Zhou said the truth.

"Because of the group structure, it is impossible to prove this problem."

Vera: "...?"