Chapter 842 Controversy?

For the mathematics community where gossip is scarce, any research progress on Riemann's conjecture will be talked about for a long time.

This is no exception for the Mathematics Department of the University of Los Angeles, Berkeley, the mecca of mathematics on the West Coast.

As early as the first time the preprint of Professor Lu's paper was posted on Arxiv, the news about the quasi-Riemann conjecture being proved was flying everywhere. If you sit in a coffee shop, you can hear people excitedly Discussing this conundrum that has lasted for a century.

"Have you heard? The Quasi-Riemann Hypothesis has been proven!"

"Just heard about it, it's unbelievable that no one has been able to shift the right border of the critical zone to the left even an iota in a century!"

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

"Hey, if only I had half the IQ of Professor Lu."

"Wake up, stop dreaming!"

Not only students in the Department of Mathematics at Berkeley, professors are also talking about this matter.

Although analytic number theory is not a strong direction of Berkeley, relatively speaking, it is more inclined to partial differential equations, but for a scholar like Terence Tao who is not proficient in almost any field, he will naturally not miss the big news in the mathematics world .

In the office of the Department of Mathematics at Berkeley, sitting in front of a desk full of draft papers, Tao Zhexuan, who was spinning a ballpoint pen, was staring at the densely packed thesis paper on the table with a frown. As for the knock on the door behind him, he didn't even hear it.

The knock on the door continued for a while, and then the door opened directly, and a tall and thin Asian man came in with a box of pizza. Judging from his skilled movements, he should be the doctor in this office.

"Professor, your pizza has arrived."

Without looking up, Tao Zhexuan said casually with his back turned to him.

"Just put it aside for me."

"Okay, although I recommend you eat it while it's hot." Putting the pizza on the table, the doctoral student glanced at the scratch paper in front of the boss, and asked curiously, "Well, what did I see this morning?" Got your thread on Mathoverflow...are you still working on that paper?"

Terence Tao: "Yes."

Swallowing, the doctoral student asked in an expectant tone.

"Is there any result?"

"I'll tell you if there is one."

"Okay." Hearing the cold voice, the doctoral student stuck out his tongue, made a helpless expression, and exited the door.

Generally speaking, Professor Tao is relatively approachable, and he is one of the few professors who can get along with students among the many big names in Berkeley.

However, this is also case by case.

Generally speaking, when he is stumped by some problem, even if his wife comes, don't expect him to be very enthusiastic...

"interesting."

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

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

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

Leaning on the office chair, staring at the dusty ceiling fan above his head, Tao Zhexuan scratched the back of his head with some nerve-wracking.

Rarely does he bother about one thing for so long.

The ballpoint pen tapped lightly on the paper, and he pondered for a while before he uttered a word with a solemn expression.

"there is controversy."

However, the tone used in this sentence was not affirmative. When dealing with this issue, he was rarely as confident as before.

"Did I read it wrong..."

Or is it really, as he thought, proving that there is a problem?

...

Speaking of which, Lu Zhou couldn't remember the last time he received Vera's email.

Maybe a year ago?

Maybe something a little longer.

Obviously, Vera, who is researching the Riemann conjecture, naturally saw the preprint he posted on Arxiv, and should have spent time researching it, and had some doubts as a result.

Many things are difficult to discuss clearly in the email, and the two agreed to have a video call at 8:00 pm Beijing time the next day.

So...

After three years, Lu Zhou once again met his most proud and most complicated disciple.

Although separated by a network cable...

At eight o'clock in the evening the next day, the video call was turned on.

After making a cup of coffee and sitting in the study, Lu Zhou was originally ready to discuss academic issues, but the atmosphere was unexpectedly stiff.

The little girl who seemed to hold back a lot of words and was going to say something, seemed not to know how to speak at the moment, so she just sat there nervously, staring straight at the computer screen without speaking.

And when Vera looked at Lu Zhou in the video with a worried face, Lu Zhou, who was also looking at Vera, had a subtle embarrassment on his face at the moment.

The golden hair is combed into a delicate princess braid, and the long skirt with silk borders outlines the curves of the shoulders. Even Lu Zhou, who can't tell the difference between the lipstick numbers, can see that this look It's obviously not everyday makeup, it's obviously well-groomed.

So what should I say at this time?

haven't seen you for a long time?

It seems a little cold.

Your new hairstyle looks great?

I always feel that there will be unnecessary misunderstandings...

Coughing lightly, Lu Zhou tried his best to make a formal expression, and spoke in a clear voice.

"Let's get right to the point...let me see where your questions lie."

Greetings and politeness will make the atmosphere a bit stiff. Everyone is engaged in mathematics, so if they go directly to the topic, it may make the atmosphere a little more relaxed.

Sure enough, with these words spoken, the atmosphere in the video call softened a little.

Vera, who was sitting at the other end of the computer, also let go, and then nodded like a chicken pecking at rice, and said in a low voice.

"Hmm, please, please wait..."

As she said that, the little girl got up and walked quickly to the side, dragging over from the edge of the classroom a blackboard filled with heartfelt writing.

Seeing the line-by-line calculation on the blackboard, Lu Zhou froze for a moment, a hint of surprise flashed in his eyes, and then his expression gradually became serious.

Looking at Lu Zhou who was deep in thought, Vera cleared her throat and continued in a low voice, "This is the algebraic geometry method you used to prove the quasi-Riemann conjecture, I tried to summarize the method from the problem itself .”

After quickly browsing the contents on the blackboard, Lu Zhou nodded approvingly and gave a positive evaluation.

"well done."

It is worthy of being the apprentice he taught.

It is not easy to sort out these things.

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

It is actually a risky thing to communicate this kind of idea with geniuses, because the academic circle only recognizes the results and does not recognize where the "Idea" comes from.

So not to mention some seemingly interesting ideas, sometimes even the staged results that are enough to be published on the top journal will be suppressed by the author himself... If he has ambitions for higher goals, but he does not belong to the The words of a scholar who is indifferent to fame and fortune and doesn't care about fame.

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

"I have carefully studied the algebraic curve on the finite field you introduced when you proved that when the value of ε is infinitesimally small, there is no non-zero trivial point of the ζ function in the region of Re(s)≥1-ε, and according to ζ( The properties of s)=2Γ(1-s)(2π)s-1sin(πs/2)ζ(1-s) get..."

Saying that, Vera turned to face the blackboard, and wrote out a line of calculations in the blank space left at the corner.

Looking at Vera's writing on the blackboard, Lu Zhou frowned slightly, but soon relaxed.

He already had a general understanding of Vera's train of thought.

On the basis of her own proof method, she gave the Plancherel formula on a kind of simply connected nilpotent Lie group through the mapping method of homology group... In short, she made some improvements to his group construction method, Then it is applied to the amplification of the value of ε.

The chalk wandering on the blackboard gradually stopped, and Vera turned around and smiled shyly.

"It's probably possible to do it this way, but I can't go on with it halfway. I think if it were you, you would be able to find the reason..."

"So... it would be great if I could help you."

In the last sentence, Vera's voice was so small that she was not sure if Lu Zhou on the other end of the video really heard it.

After staring at the formula on the blackboard for a while, Lu Zhou, who was sitting there motionless, suddenly spoke.

"Do you know why there is no reason?"

Slightly stunned, Vera asked subconsciously.

"……why?"

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

"Because the group construction method cannot prove this problem."

Vera: "...?"