Chapter 832 Clues to the Riemann Hypothesis

Inspiration is often born inadvertently.

In the previous class, Lu Zhou recalled many details that he had overlooked when studying the problem by sorting out the past and present of the Riemann conjecture.

Although many times, these details are irrelevant even if you think about them, but at critical moments, these insignificant clues can also play an amazing role.

After returning to the office, Lu Zhou sat down at the desk, took out the draft paper from the drawer, and wrote down the things he thought of earlier, line by line.

"The Riemann conjecture is a conjecture proposed to study the π(x) function. Riemann's pioneering work is not to propose the Riemann conjecture, but to introduce the method of the Riemann zeta function to integrate the π(x) The study is lifted from the real straight line to the complex plane."

The tip of the pen slid across the paper, and Lu Zhou wrote down a line of calculation smoothly.

[π(x)=∫dt/lnt+O(x^(1/2+ε))……]

"The equivalence problem of Riemann's conjecture," he stopped the pen in his hand, tapped the paper with the tip of the pen, and Lu Zhou's expression gradually showed a contemplative solemnity, and he said to himself thoughtfully, " If the Riemann conjecture is established, the asymptotic formula is also valid, and in turn, the asymptotic formula can also be used to deduce the Riemann conjecture..."

"The key to solving the problem should lie in the π(x) function itself!"

Gradually a sliver of understanding came into my mind, but I always felt that something was missing.

It's like a jigsaw puzzle that has been put together one-third of the way, and there are scattered pieces beside it. It seems that nothing is missing, but the most critical key is missing.

Find it and it will tie all the clues together, but if you can't find it, everything seems to be just talk.

After working at the desk like this for an hour, Lu Zhou didn't come back to his senses until his stomach made a soft "goo".

And when he moved his eyes from the desktop to the fading dusk outside the window, he unexpectedly discovered that he had sat at the desk for so long without knowing it.

"I saw that you were too focused, so I didn't have the heart to call you." At about this time, Assistant Lin's voice floated from the side, "Are you planning to go to the cafeteria later?"

Turning his eyes away from the night that was gradually climbing up to the horizon from the window, Lu Zhou looked at Assistant Lin who was standing at the door, thought for a moment and said, "If you plan to go to the cafeteria, bring me some food."

He probably planned to stay in the office for a while, in order not to interrupt the train of thought that he had finally grasped, he planned to go back later.

Lin Yuxiang blinked and asked, "Barbecue with rice?"

Lu Zhou glanced at her unexpectedly

"...how did you know I was going to say this?"

Lin Yuxiang pursed her lips and smiled slightly: "Guess~"

For some reason, Lu Zhou felt goosebumps all over his body when he saw her face knowing him well, so he coughed lightly and said.

"Suddenly I don't want to eat barbecue bibimbap tonight. Help me bring the braised chicken and rice... Thank you."

After being stunned for two or three seconds, Lin Yuxiang gave Lu Zhou a resentful look, turned around and walked away.

Didn't have to wait long.

Lu Zhou, who was sitting at the desk, continued to calculate on the draft paper for a while. Assistant Lin, who had eaten in the cafeteria, quickly came back with a box of braised chicken and rice, and delivered the takeaway to Lu Zhou's table. superior.

After opening the lid of the packing box, the strong smell of chicken juice came to his face. Looking at the tender yellow chicken and the red and green peppers, Lu Zhou suddenly moved his index finger and tore apart the disposable tableware. , Scooped a spoonful of soup with a spoon and poured it on the plump grains of white rice, and ate it hungrily.

Perhaps because he was usually busy, Lu Zhou found that he seemed to have a soft spot for fast food. I used to eat bacon sandwiches when I was in Princeton, but when I returned to China, it was either bibimbap, or something similar to bibimbap.

Although this diet is not very healthy from a nutritional point of view, this high-quality and cheap satiety can bring people unexpected satisfaction, just like instant coffee.

Anyway, he is the type who doesn't gain weight no matter what he eats, coupled with the system-enhanced metabolism, it doesn't seem to be a problem if he eats casually?

After finishing dinner in a hurry, Lu Zhou turned on the computer. After conceiving for a while, he tapped the keyboard quickly with his ten fingers, converting the previously conceived content into a line of papers.

Although these things may be just some trivial ideas, every substantive progress in the research on ζ(s) will bring a huge impetus to the research of prime number distribution theory, so no matter how trivial the idea is, it also has its value of.

Regardless of whether these things can resonate with other scholars and create more intense sparks in the collision of ideas, Lu Zhou intends to post these contents on Arxiv.

After browsing the papers of other scholars on the Internet for a while, when Lu Zhou was about to turn off the computer, pack up his things and go home, he suddenly received an unexpected video call.

The video request was sent by his former student Qin Yue.

After pressing the connected button, Lu Zhou smiled and greeted the familiar face that appeared on the other side of the screen.

"How have you been? Is your job as a lecturer at Princeton going well?"

The background in the video is morning.

The man sitting in front of the camera looked the same as he did four years ago. It's just that compared with four years ago, it looks a little less dull and a little more calm.

Looking at the mentor sitting in front of the camera, Qin Yue smiled and said: "It went very well, remember the membership of the Ivy League club? I got it the second year after you left."

"They won't reject a mathematician who once proved Kakutani's conjecture," Lu Zhou joked, and continued after a short pause, "Is there anything wrong with calling me suddenly?"

Most people who do mathematics don't have any twists and turns, and they speak more directly. Pushing the glasses on the bridge of the nose, Qin Yue asked straight to the point.

"Have you been studying the Riemann Hypothesis recently?"

Lu Zhou: "...what's wrong?"

Qin Yue smiled a little embarrassedly: "It's nothing, I just saw on your personal homepage that there was an additional review record on your academic resume, which was related to the Riemann conjecture, so I was a little curious."

Lu Zhou didn't know whether to laugh or cry: "...you discovered this?"

Oh my god, you have to pay attention to me?

Generally, academic resumes such as manuscript review records are not for applying for jobs in research institutions or something. Generally, who would stare at this stuff?

Looking at Lu Zhou with a surprised face, Qin Yue made a helpless expression: "I dare say that more than half of the scholars in the entire mathematics world are watching your movements, and I am definitely not the only one doing this."

Although I always feel that there are slots everywhere, Lu Zhou didn't know where to complain for a while.

Opening his mouth, he nodded and approved Qin Yue's guess.

"...I've been really researching the Riemann Hypothesis recently."

As soon as he heard that his former mentor was indeed trying to break through this century-old problem that had plagued the mathematics world for a century and a half, Qin Yue suddenly showed interest on his face, and sat up straight and asked.

"Any clues... I mean, do you need my help?"

In the middle of speaking, he suddenly realized that his request was a bit presumptuous for a scholar, so he immediately changed his words.

But Lu Zhou didn't care too much, just smiled and said.

"There are some clues, especially after reading Molina's paper, I am more sure of my guess."

Qin Yue: "what guess... Is it convenient for me to know?"

"There is nothing inconvenient. If you can prove the Riemann conjecture according to my thinking, I will be happy for you," Lu Zhou smiled and continued, "Come back to business, according to my observations, or guesses, through More interesting conclusions may be obtained by advancing the method of lower bound estimation of the zero-point ratio on the critical line, but it is unrealistic to use this method to solve the Riemann Hypothesis itself."

Hearing this sentence, Qin Yue's expression gradually became serious.

The method of advancing the lower bound estimation of the zero point ratio on the critical line can be said to be one of the mainstream methods for researching Riemann's conjecture at present, and the current "best" result of Riemann's conjecture is also proved by this method. of.

However, Lu Zhou now said that this route might not work. Although in terms of his status, it would not make this statement sound unbelievable, but it still surprised Qin Yue.

"what do you mean……"

Lu Zhou said in a serious tone: "Maybe we have to return to the π(x) function itself to find the last piece of the puzzle."

-

(Thanks to the leader of the book friend "Zhong Kui Trumpet" for the reward~~~)