Chapter 831: Clue for the Riemann Hypothesis
Inspiration always arrived at unexpected times.
Lecturing about the history of the Riemann hypothesis had pointed out some of the details that he ignored when conducting research.
Even though most of the time these details were useless, these irrelevant clues could occasionally play an important role.
After Lu Zhou returned to his office, he sat down at his desk and pulled out a piece of draft paper. He began writing down his thoughts.
“The Riemann hypothesis was proposed to study the π(x). Riemann’s pioneering work wasn’t on the proposal of the Riemann hypothesis, but it was on using Riemann zeta function to increase the domain of π(x) to complex numbers.”
Lu Zhou’s pen glided on the paper. He wrote down a line of the equation.
[π(x)=∫dt/lnt+O(x^(1/2+ε)]
“Riemann hypothesis’ equivalence problem,” Lu Zhou said as he placed the tip of the pen on the paper. He said to himself, “If the Riemann hypothesis is true, then we can drive this asymptotic formula from the Riemann hypothesis…
“The key to solving this problem is the function π(x) itself.”
He felt like he was missing something.
It was almost like he was a third of the way done with a jigsaw puzzle, with the rest of the pieces scattered nearby. He just needed to connect the rest of the pieces. He needed a clue.
With that clue, he could connect the rest of the pieces.
Lu Zhou sat in front of his desk for an hour or so. His stomach began to rumble.
He looked outside and saw the sunset outside his window. He finally realized how long he had been sitting there.
“You were too focused, I didn’t want to interrupt you,” a.s.sistant Lin said. “Do you plan on going to the cafeteria?”
Lu Zhou looked at a.s.sistant Lin, who was standing at the door, and he thought for a second before saying, “If you’re going to the cafeteria, bring me something.”
He planned on staying in the office for a bit longer as he didn’t want his thoughts to be interrupted.
Lin Yuxiang blinked and said, “Barbecued meat on rice?”
Lu Zhou looked at her.
“How did you know I wanted that?”
Lin Yuxiang winked and said, “I guessed it.”
Lu Zhou felt a little creeped out. Lin Yuxiang gave him the chills.
“I don’t want barbecued meat on rice tonight. Can you bring me some spicy chicken on rice… Thanks.”
Lin Yuxiang glanced at Lu Zhou with a hint of resentment. She then turned around and left.
He didn’t have to wait for long.
Lu Zhou was still sitting at his desk, writing formulas on a piece of draft paper, when a.s.sistant Lin, who just came back from the cafeteria, placed a takeaway box of spicy chicken on rice on Lu Zhou’s table.
Lu Zhou opened the takeaway box and looked at the tender chicken mixed with red and green peppers. He opened the pack of disposable utensils, placed some chicken on the rice, and began eating.
Because of his busy schedule, Lu Zhou had a fondness toward fast food. In Princeton, he would only eat bacon sandwiches, and in China, he would only eat meat on rice at the cafeteria.
Even though his diet wasn’t healthy from a nutritional point of view, these inexpensive meals made him feel satisfied. It was just like instant coffee.
Not to mention, his metabolic capacity was strengthened by the system, so he didn’t have to care about his diet.
Lu Zhou quickly finished his meal. He opened his computer and contemplated it for a moment. His ten fingers quickly tapped on the keyboard as he transformed his thoughts into words.
Even though his ideas might be trivial, any progress on the ζ(s) function would contribute to the research of prime numbers. Therefore, even trivial ideas had a certain amount of value.
Lu Zhou didn’t care if his ideas would inspire other scholars, he was going to upload this onto arXiv regardless.
After reading some theses from other scholars, Lu Zhou turned off his computer and planned on going home. However, he suddenly received a video call.
Qin Yue was the person video calling him.
Lu Zhou pressed the “Accept” b.u.t.ton and saw a familiar face appear in front of him.
“How’s it going? How’s lecturing at Princeton?”
It was morning over in Princeton.
The man sitting in front of the camera looked exactly the same as he did four years ago, just with a little more confidence.
Qin Yue looked at his ex-supervisor and said, “It’s been going great. Remember the Ivy Club club? I was accepted a year after you left.”
“They obviously aren’t going to reject a mathematician who proved the Collatz conjecture.” Lu Zhou smiled and said, “Is there something you want to talk about?”
Mathematicians generally didn’t like small talk. Qin Yue adjusted his gla.s.ses and asked, “I heard you’re researching the Riemann hypothesis?”
Lu Zhou: “… Yeah, why?”
Qin Yue smiled awkwardly and said, “Nothing, I just saw that you reviewed a thesis related to the Riemann hypothesis. I was just curious.”
Lu Zhou smiled and said, “You found out about that?”
Jesus, is he stalking me?
It was very rare for someone to look at someone else’s academic review record.
Qin Yue looked at Lu Zhou and said, “I promise the majority of mathematicians are stalking you. I’m not the only one.”
Lu Zhou felt a little weird, but he didn’t know what to say.
He nodded and replied, “… I have been researching the Riemann hypothesis.”
When Qin Yue heard that his former supervisor was trying to solve this century-old problem, a look of interest appeared on his face.
“How’s the progress—I mean, do you need my help?”
Halfway through his sentence, he realized it was inappropriate to ask how the progress was going, so he changed his words.
However, Lu Zhou didn’t seem to care.
“I have some clues, especially after reading Molina’s thesis. That further confirmed my guess.”
Qin Yue: “What guess… Are you allowed to tell me?”
“Of course I am. If you can prove the Riemann hypothesis using my guess, I would be happy.” Lu Zhou smiled and said, “My guess is that, the method of lowering the lower bound estimation of the zero points on the critical line might lead to some interesting conclusions, but it is unrealistic to solve the Riemann hypothesis using this method.”
Qin Yue had a serious look on his face.
Lowering the lower bound of the zero points on the critical line was one of the most popular methods for researching the Riemann hypothesis. The “closest” result in proving the Riemann hypothesis was proved using this method.
However, Lu Zhou said this method might not work, which surprised Qin Yue.
“What do you mean?”
Lu Zhou said in a serious tone, “We might have to research the π(x) function itself to find the last puzzle piece to solve this problem.”