Chapter 838 The Method of Approaching From the Boundary!

After successfully killing time on the balcony, the banquet was over, and after leaving two banknotes on the hotel waiter's tray, Lu Zhou immediately went to the parking lot and got into the waiting black red flag.

"Back to Zhongshan International."

"OK."

Wang Peng, who was sitting in the driver's seat, nodded, and quickly started the car and drove on the road.

Although when discussing the Riemann zeta function with the lady with a long name, he basically talked there on his own, but even he himself did not expect that this kind of discussion about cows and pianos can be used. It gave him some inspiration.

Sitting in the back row of the car, Lu Zhou, who had been silent for a long time, suddenly said something.

"I still lack one tool."

Wang Peng, who was holding the steering wheel, was slightly stunned.

"... what tool?"

"nothing."

"Need to go to the supermarket?"

Lu Zhou smiled and shook his head.

"It would be great if the supermarket sold them."

He had a premonition that if he was allowed to continue talking, he might be in a daze for the rest of the journey. Considering that he was still driving, Wang Peng wisely shut his mouth and stopped talking, and focused his attention on the road. concentrated on the road ahead.

The location of Zijinshan Hotel is not far from Zhongshan International, but after a ten-minute drive, Lu Zhou quickly saw the familiar gate of the community.

The car stopped at the door of the house, and after explaining that he didn't need to look for him tomorrow, Lu Zhou went straight back home and walked to the stairs quickly.

"It is unrealistic to solve the π(x) function by a general method. There are not 10,000 people who have challenged this difficult problem in the past century and a half. Even if this idea is feasible, the traditional method cannot It must have been considered."

"Disruptive outcomes often require disruptive approaches to solve."

"I need new tools!"

The quadrotor drone whimpered beside it, and followed Lu Zhou up to the second floor staggeringly.

Since she couldn't recognize the command contained in Lu Zhou's self-talk, Xiao Ai who followed behind asked curiously.

"Owner?"【()】

"Make me a cup of coffee, instant one, just send it to the study."

"But it's already so late..."【(°ー°〃)】

"It's okay, I didn't plan to sleep tonight."

"Good master, but please take care of your body."【(=ω)】

Stretching out his hand and pushing open the door of the study, Lu Zhou only dropped three words and walked in quickly.

"understood!"

It is unrealistic to climb the Mount Everest conjectured by Riemann at one time. This Mount Everest has stood at the top of the mathematics world for too long. Countless people have tried to challenge it, but most of them are at the foot of the mountain. Turn around, so that although latecomers can find a lot of road signs pointing to the top of the mountain, but there is not even a ladder to borrow.

No matter which proof idea is adopted, the original road must be repaired before reaching the top of the mountain.

At least, let him see the hope of proof...

Sitting down in front of the desk, he crushed all the draft papers piled up at the corner of the table and threw them into the wastebasket. Lu Zhou took out a new stack of draft papers and piled them on the table.

Looking at the already full wastebasket and the pile of draft paper on the table that was about to be filled, a smile suddenly appeared on the corner of Lu Zhou's mouth, shaking his head and talking to himself.

"...This is probably the most economical project I have done in these years."

Even when he was proving the Yang-Mills equation by linking the strong interaction force and the electromagnetic force, he wrote to borrow CERN equipment to do several sets of theoretical physics experiments, and spent a lot of money.

But for a purely mathematical problem like Riemann's conjecture, I am afraid that only scratch paper and brain cells are needed...

...

For Lu Zhou, it seemed a long time ago that he devoted himself to the research of a subject.

Since serving as the chief designer of the Lunar Orbit Construction Committee, he has mostly played the role of an academic leader, and rarely rushes to the forefront of scientific research like ordinary scientific research dogs.

However, even so, the familiar feeling is not unfamiliar to Lu Zhou.

Especially when he devotes himself wholeheartedly to the problem on the paper, the strings of Arabic numerals and ancient Greek symbols flowing from his pen are like the notes of classical music, combining cheerful rhythm and serious rhythm. Together, they form a silent but soul-stirring symphony.

The mist rising from the coffee cup gradually dissipated, the street lights beside the asphalt path gradually went out, and the Zijin Mountain under the night was completely quiet. Then, at some time, the morning light of dawn gradually appeared outside the window, as if caught by those few sounds. Disturbed by the crisp birdsong, Lu Zhou lightly stopped the ballpoint pen in his hand, and said softly in his mouth.

"In the study of Weil's conjecture including the 'cottage version' Riemann conjecture, Grothendieck created a new mathematical tool, the tale cohomology method, which has had a huge impact on the development of algebraic geometry and even the entire field of mathematics. impetus, and eventually led directly to the proof of Deligne's Weil conjecture."

"If you want to find the way to the top of the mountain, you have to take down the nearest mountain first... a weak conjecture of Riemann's conjecture."

Just like the relationship between the twin prime conjecture and the Polignac conjecture, the latter is a relationship contained in the former. Although the proof of the former cannot directly lead to the proof of the latter, it can provide inspiration for the proof of the latter effect.

Such is the case with exploration in the field of mathematics.

From the weak form of a conjecture to the conjecture itself, and the strong conjecture that is promoting the conjecture itself, when all the problems are solved and all the clues are connected together, a mathematical building is also built.

Thinking of this, Lu Zhou pushed aside the full draft paper and wrote a line of calculations on the paper.

【Re(s)=1-c/ln[|Im(s)|+2](>0)...】

A smile gradually appeared on the corner of his mouth, and the seriousness that was pent up between Lu Zhou's brows also dissipated a lot.

"If you want to prove that all the zero points are distributed on the zero boundary, you can start by excluding areas where there are no zero points! Re(s≤0 and Re(s)≥1 are known results, as long as you find a way to advance this conclusion to All areas outside the critical line, that is, Re(s)<1/2 and Re(s)>1/2! can prove the Riemann Hypothesis!"

"I can start on the right border first!"

This line of proof is also known as the critical band method! Different from proving how many percent of the zero points are on the zero boundary, the core of the whole proof idea is to shrink the area of ​​the critical zone containing all the zero points and finally approach the position of the critical line!

As long as he can translate the right boundary of the critical zone from Re(s)=1 to Re(s)=1-ε(ε>0) to the left, so as to exclude the area where Re(s)≥1-ε, No matter how small the value of ε is, it can play a huge role in promoting the proof of the Riemann Hypothesis!

The idea is already there, now it is left to solve this problem!

Although it was just an intuition, this intuition told him that this piece of the puzzle was likely to be in algebraic geometry! Coincidentally, this is also the area where he is least proficient...

"It would be nice to have someone to discuss it with."

However, just as he had this thought, Lu Zhou immediately shook his head.

Especially Professor Deligne...

But unfortunately, some things cannot be clearly stated in emails. Video calls may be a method, but whether it is the atmosphere or the feeling, it is definitely not more suitable for academic exchanges than the afternoon tea time in Princeton.

At present, the only thing he can rely on is himself.

"You can't depend on others."

However, having said that, in the end Lu Zhou couldn't hold back his curiosity. He turned on his computer and logged on to the Mathoverflow page to search for recent topics.

But soon, obvious disappointment appeared on his face.

He had previously hung that paper on Arxiv, and he also expected to be able to play a role in attracting jade, and by triggering related discussions on Mathoverfolw, he could see some interesting ideas.

But now it seems that his idea is obviously in vain.

Even in a relatively professional mathematics discussion community, the last time it is a PHD, people's nature is more keen on gossip than solving specific problems.

Although there are also some discussions focused on the academic field, the content of these discussions is a bit too "outdated".

"Looks like it's going to be closed for a few days."

Stretched and leaned back on the chair, Lu Zhou picked up his phone from the table and sent a text message to Wang Peng, telling him not to look for him for a few days, then got up yawning and went downstairs to the bathroom .

At the beginning, he was hoping that he would be able to grasp something with that sliver of inspiration at night, and even get a phased result out, but unfortunately, the situation was much more serious than he had imagined, at least not with a little inspiration. It can be done with a little inspiration and a night's time.

Now that he has decided to retreat, naturally there is no need to fight for that day and night.

Before starting the official work, he planned to make up for the sleepless night yesterday...