Inspiration is often born by accident.

Previously, in class, Lu Zhou recalled many details that he had overlooked when studying the problem by sorting out the past and present lives of Riemann's conjecture.

While many times these details are inconsequential, they can also be surprising in critical moments.

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

"The Riemann conjecture was proposed for the study of the π (x) function, and Riemann's pioneering work did not lie in proposing the Riemann conjecture, but by introducing the method of the Riemann zeta function, the study of π(x) was elevated from a real straight line to a complex plane."

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

【π(x)=∫dt/lnt+O（x^（1/2+ε））……】

"The equivalence of the Riemann conjecture," stopped the pen in his hand, lightly tapped the paper with the tip of the pen, Lu Zhou's expression gradually appeared a touch of contemplative solemnity, and said to himself thoughtfully, "If the Riemann conjecture is true, the asymptotic formula is also true, and in turn, the Riemann conjecture can also be deduced from this asymptotic formula......"

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

A hint of enlightenment gradually appeared in my heart, but I always felt that there was still something missing.

It's as if a puzzle piece that has been put together a third of the way is scattered with bits and pieces, as if nothing is missing, but only the most crucial key is missing.

If you find it, you can tie it all together, and if you can't find it, everything seems to be just empty talk.

I did this at my desk for an hour, and it wasn't until there was a soft "grunt" in my stomach that Lu Zhou suddenly came back to his senses.

And when he moved his gaze from the desktop to the twilight that was fading away from the window, he was surprised to find that he had been sitting at the desk for so long without realizing it.

"Seeing that you are too focused, I am reluctant to call you," At about this moment, Assistant Lin's voice floated over from the side, "Are you going to go to the cafeteria in a while?" ”

Retracting his gaze from the window and gradually climbing to the sky, 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 the food." ”

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

Lin Yuxiang blinked and asked, "Barbecue bibimbap?" ”

Lu Zhou glanced at her unexpectedly

“…… How do you know I'm going to say this? ”

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

I don't know why, looking at her look that understands herself very well, Lu Zhou felt goosebumps all over his body, so he coughed lightly and said.

"I suddenly don't want to eat bibimbap tonight, so please bring me the yellow braised chicken rice...... Thank you. ”

After being stunned for two or three seconds, Lin Yuxiang glanced at Lu Zhou resentfully, turned around and walked away.

There was no long wait.

Lu Zhou, who was sitting at the desk, continued to perform calculations on the draft paper for a while, and Assistant Lin, who had gone to the cafeteria to eat, quickly walked back with a box of yellow braised chicken rice and delivered the takeaway to Lu Zhou's table.

Looking at the tender yellow chicken and the red and green chili peppers, Lu Zhou's index finger suddenly moved, and he tore open the disposable tableware with a spoon, scooped a spoonful of soup and poured it on the plump white rice, and devoured it.

Perhaps because he was usually busy, Lu Zhou found that he seemed to have a soft spot for fast food. I used to have a bacon sandwich when I was in Princeton, and when I returned home, it was either bibimbap or something like bibimbap.

Although this diet is not very healthy from a nutritional point of view, this kind of satiety at an affordable price can bring unexpected satisfaction, just like instant coffee.

Anyway, he is the type who doesn't grow meat no matter how he eats, and coupled with the metabolic ability that has been strengthened by the system, it doesn't seem to be in the way of eating casually?

After hastily settling dinner, Lu Zhou turned on the computer, and after a moment of thinking, his ten fingers tapped quickly on the keyboard, transforming the previously conceived content into lines of papers.

Although these things may be just trivial ideas, every substantial progress in the study of ζ(s) will bring a huge impetus to the study of the distribution theory of prime numbers, so even the smallest idea has its value.

Regardless of whether or not these things can resonate with other scholars, and create more violent sparks in the collision of ideas, Lu Zhou intends to hang these contents on Arxiv.

After browsing the papers of other scholars on the Internet for a while, just as Lu Zhou was about to turn off the computer and 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.

casually pressed the connected button, looking at the familiar faces that appeared on the other side of the screen, Lu Zhou smiled and said hello.

"How's it going? Is it still going well as a lecturer at Princeton? ”

The background in the video is the morning.

The man sitting in front of the camera doesn't look the same as he did four years ago. It's just that compared to four years ago, it looks a little less wooden and a little more calm.

Looking at the mentor sitting in front of the camera, Qin Yue smiled and said, "It's very smooth, do you remember the members of the Ivy League Club?" I got it the year after you left. ”

"They wouldn't refuse a mathematician who once proved Kakutani's conjecture," Lu Zhou joked, pausing for a moment before continuing, "Is there anything wrong with calling me suddenly?" ”

Most of the people who are engaged in mathematics don't bend their bowels, and they all speak more directly, pushing down the glasses on the bridge of their noses, Qin Yue asked straight to the point.

"You've been working on the Riemann hypothesis lately?"

Lu Zhou: "...... What's wrong? ”

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

Lu Zhou cried and laughed: "...... Did you find out about this? ”

Mom, do you have to pay attention to me?

Generally, the reviewer records this kind of academic resume, not to go to a research institution to sign up for a job or something, who would generally stare at this thing?

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

Although he always felt that everywhere was a slot, Lu Zhou didn't know where to complain for a while.

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

“…… I've really been working on the Riemann hypothesis lately. ”

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

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

In the middle of his sentence, he suddenly realized that his request was a bit presumptuous for a scholar, and he immediately changed his tune.

However, 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's nothing inconvenient, I'll be glad for you if you can prove the Riemann hypothesis according to my train of thought," Lu Zhou smiled and continued, "To get back to the point, according to my observations, or guesses, there may be more interesting conclusions to be drawn by advancing the method of estimating the lower bound of the zero-point ratio on the critical line, but it is unrealistic to solve the Riemann hypothesis itself through this method." ”

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

It can be said that the method of estimating the lower bound of the zero point ratio on the critical line is one of the mainstream methods for studying the Riemann hypothesis, and the current "best" results of the Riemann hypothesis are also proved by this method.

However, Lu Zhou now said that this route might not work, although in terms of his status and status, it didn't make this sentence sound incredible, but it really made Qin Yue a little surprised.

"What do you mean ......"

Lu Zhou said in a serious tone: "Maybe we have to go back to the π (x) function itself in order to find the last piece of the puzzle to solve this problem." ”

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