Inspiration was often born inadvertently.
When Lu Zhou was in class, he tried to sort out the Riemann's conjecture and recalled some of the details that he had overlooked.
Although most of the time, these details were insignificant, at critical moments, these insignificant clues could play an astonishing role.
After Lu Zhou went back to his office, he sat down at his desk and took out a piece of draft paper from his drawer. He began to write down the ideas that he had previously thought of.
"The Riemann's conjecture is a conjecture that was proposed to study the π (x) function. Riemann's groundbreaking work wasn't in proposing the Riemann's conjecture, but rather, it was in introducing the Riemann zeta function, which elevated the study of π (x) from the real line to the complex plane."
The tip of the pen gently slid across the paper and Lu Zhou smoothly wrote down a line of calculations.
[π (x) = ldt/lnt + O (x ^ (1/2 + ε)) …]
"The equivalence problem of the Riemann's conjecture." Lu Zhou stopped writing and gently tapped the paper with the tip of the pen. He had a solemn expression on his face as he said, "If the Riemann's conjecture is true, then the asymptotic formula is also true. Conversely, this asymptotic formula can also be used to deduce the Riemann's conjecture …
"The key to solving the problem should be the π (x) function itself!"
There was a hint of enlightenment in his heart, but he still felt like he was missing something.
It was like a one-third completed jigsaw puzzle with bits and pieces scattered around it. It seemed like nothing was missing, but the most critical key was missing.
If he found the key, he could connect all the clues together. If he couldn't find it, everything seemed to be empty talk.
Lu Zhou sat in front of his desk for an hour until his stomach made a soft growling sound, and he suddenly came back to his senses.
When he shifted his gaze from his desk to the fading dusk outside the window, he was surprised to find that he had been sitting at his desk for a long time.
"You were too focused, so I didn't want to wake you up." Assistant Lin's voice came from the side, "Are you going to the cafeteria later?"
Lu Zhou looked at Assistant Lin, who was standing at the door. After thinking for a moment, he said, "If you plan to go to the cafeteria, bring some food for me."
He probably planned to stay in the office for a while. In order not to interrupt his train of thought, he planned to go back a little later.
Lin Yuxiang blinked and asked, "Barbecue on rice?"
Lu Zhou looked at her in surprise.
"… How did you know I was going to say this?"
Lin Yuxiang smiled and said, "I guessed ~"
For some reason, Lu Zhou felt goosebumps all over his body when he saw her look as if she knew him very well, so he coughed lightly and said.
"I suddenly don't feel like eating barbecue on rice tonight, bring me some braised chicken and rice … Thanks."
Lin Yuxiang paused for a few seconds and rolled her eyes at Lu Zhou. She then turned around and walked away.
Lu Zhou didn't have to wait for long.
Lu Zhou was sitting at his desk. He continued to calculate on a piece of draft paper for a while. Assistant Lin, who went to the cafeteria to eat, quickly came back with a box of braised chicken and rice. He placed the takeout on Lu Zhou's desk.
When he opened the box, the rich smell of chicken juice wafted out. Lu Zhou looked at the tender yellow chicken and red and green peppers. He suddenly became hungry, and he quickly put away the disposable utensils. He scooped up a spoonful of soup and poured it on the rice. He then began to gobble it down.
Perhaps it was because he was usually busy, but Lu Zhou found that he seemed to have a special fondness for fast food. When he was in Princeton, he used to eat bacon sandwiches. When he went back to China, he would either eat barbecue on rice or something similar.
Although from a nutritional point of view, this kind of diet was not very healthy, this cheap and delicious feeling of fullness could bring unexpected satisfaction, just like instant coffee.
Anyway, no matter how much he ate, he wouldn't gain weight. Plus, his metabolism was strengthened by the system, so it didn't matter if he ate a casual diet.
Lu Zhou quickly finished his dinner and turned on his computer. After thinking for a while, his fingers began to type on the keyboard. He turned his previous ideas into a thesis.
Even though these ideas might only be trivial, every substantial progress in the study of ζ (s) would bring a huge boost to the study of the distribution of prime numbers. Therefore, even the most trivial ideas had their value.
Regardless of whether or not these ideas could resonate with other scholars, Lu Zhou planned on posting these ideas on arXiv.
Lu Zhou browsed through other scholars' theses online. He was about to turn off his computer and go home when he suddenly received an unexpected video call.
The video call request was from his former student, Qin Yue.
Lu Zhou pressed the answer button and looked at the familiar face that appeared on the other end of the screen. He smiled and said hello.
"How have you been? Is your job as a lecturer at Princeton going well? "
The background of the video was in the morning.
The man sitting in front of the camera looked the same as four years ago. It was just that compared to four years ago, he looked a little less wooden and a little more mature.
Qin Yue looked at his supervisor sitting in front of the camera and smiled as he said, "It's going very well. Do you remember the Ivy Club membership? I got it the year after you left. "
"They won't reject a mathematician who proved the Collatz conjecture," said Lu Zhou jokingly. He paused for a second and said, "Why did you call me?"
Most mathematicians were straightforward and straightforward. Qin Yue pushed his glasses up the bridge of his nose and went straight to the point.
"You've been researching the Riemann conjecture?"
Lu Zhou: "… Why?"
Qin Yue smiled embarrassedly and said, "Nothing, I just saw a review record on your academic resume. It's related to the Riemann conjecture, so I'm a bit curious."
Lu Zhou was dumbfounded. He said, "… You noticed that?"
Oh my god, is she following me?
Normally, if you didn't go to a research institute to apply for a job, who would pay attention to a thesis review record?
Qin Yue looked at Lu Zhou and said, "I dare say that more than half of the mathematics community is following you. I'm not the only one."
Even though Lu Zhou felt like there was something wrong with Qin Yue, he didn't know where to start.
He opened his mouth and nodded. He agreed with Qin Yue's guess.
"… I've been researching the Riemann conjecture recently."
When Qin Yue heard that his former supervisor was trying to solve this century-old conjecture problem, he suddenly had a look of interest on his face.
He sat up straight and asked, "Do you have any clues … I mean, do you need my help?"
He suddenly realized that his request was a bit presumptuous for a scholar, so he immediately changed his words.
However, Lu Zhou didn't mind. He smiled and said, "I have some clues.
"There are some clues. After reading Molina's thesis, I'm even more certain of my guess."
Qin Yue: "What guess … Do I know?"
"It's not inconvenient. If you can prove the Riemann conjecture using my ideas, I'll be happy for you." Lu Zhou smiled and said, "Back to the main topic. According to my observations, or my guesses, I might be able to obtain more interesting conclusions by advancing the lower bound of the zero-point ratio on the critical line. However, solving the Riemann conjecture using this method is unrealistic."
Hearing this, Qin Yue's expression gradually became serious.
The method of advancing the lower bound of the zero-point ratio on the critical line was one of the mainstream methods for researching the Riemann conjecture. The "best" result for the Riemann conjecture was also proven using this method.
However, Lu Zhou was now saying that this method might not work. Even though Lu Zhou's words didn't sound ridiculous, Qin Yue was still a little surprised.
"So what you're saying is …"
Lu Zhou said in a serious tone, "Maybe we have to go back to the π (x) function itself to find the last piece of the puzzle."
(Thank you to the Chief of Zhong Kui's alternate account for the tip ~ ~ ~)
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