The corners of Vera's mouth curled up into a happy smile when she heard the compliment.
To her, this was undoubtedly the best compliment in the world.
She stood next to Lu Zhou and spoke softly.
"Your guess is correct. The Collatz conjecture is a number theory problem, but it is also a complex analysis problem …"
As early as 199 and G. Meinardus proved that the 3n + 1 conjecture is equivalent to the functional equation h (where λ = e ^ (2πi/3)) in the unit disk < 1}, and the analytic solution is in the form h. (h0 and h2 are complex constants)
On top of this, Schleicher and others proved in 1998 that any entire function h (z) made g (z) = z/2 + (1? cosπz)(z+1/2)/2+1/π(1/2? Cos π z) sin π z + h (z) sin2π z satisfied: N? Φ (g).
Based on these two conclusions, Vera constructed a clever transcendental entire function and proved that there was an entire function h (z). For every branch D of g (z) and Φ (g) containing a positive integer, there existed z0 ∈ D, such that {g ^ ok (z0)} ∞/k = 1 converged to 1.
It was not difficult to deduce that the Collatz conjecture was established!
"Excellent proof …" Lu Zhou said with a smile on his face. He said from the bottom of his heart, "Amazing."
From the summer of '16 to the end of' 17.
He was happy to see that his student had grown up.
He was also happy to see that his "Group Structure Method" theory for additive number theory did not stop at Goldbach's conjecture. Not only that, but it was also passed on to his student.
Now, he had some understanding of the "joy" described by the System, and what kind of feeling it was.
"… Thanks to your guidance," said Vera humbly. Her eyes were filled with gratitude.
Even though she completed the process, the entire proof idea was provided by Lu Zhou.
From the in-progress results at the Berkeley report at the beginning of the year to the final proof with Qin Yue and Hadi, all of her work revolved around this idea.
She, who had walked all the way to the end, knew better than anyone how important these obscure jobs were.
Lu Zhou smiled and said, "Don't be humble, I only provided the direction. You're the one running to the finish line."
He paused for a second and said, "… About this thesis, I suggest you submit it to Annual Mathematics. However, the editorial department is on vacation these days, so you can upload it to arXiv … Maybe the editors of Annual Mathematics will give up their vacation for you."
Uploading the thesis on arXiv as a preprint could be useful, but it didn't really matter if it wasn't uploaded. The Collatz conjecture was very popular in the 80s and 90s, but it wasn't a popular research direction now. The chances of it being a scam were almost zero.
The reason why Lu Zhou made this suggestion was because he had his own selfish reasons.
Based on the inference he made when he solved Goldbach's conjecture, the system used the time the thesis was published as a benchmark.
Therefore, as long as the thesis was uploaded to arXiv, the mission would be considered complete.
After hearing Lu Zhou's suggestion, Vera nodded seriously.
"I understand, I'll do it right away."
Lu Zhou smiled and said, "Okay then, I'll erase the equations on the blackboard for you … Thank you for the gift."
Hearing this praise, Vera's face revealed a happy smile.
After a while, she suddenly lowered her head, her cheeks blushing imperceptibly.
"Professor."
Lu Zhou: "What?"
She gathered her courage and looked at Lu Zhou.
"Can I … make a wish?"
"I'm not Santa Claus, I can't put what you want in the sock on your bedside table." Lu Zhou joked and paused for a second. He then said, "However, as long as it's not against my principles, I'll definitely help you."
"I …"
Vera opened her mouth.
However, at this moment, she suddenly realized that her feelings might cause trouble for him.
She was about to say something, but she couldn't say it.
"I … want to study your PhD."
Lu Zhou paused for a second and smiled. "You're welcome to do so! If you suddenly want to change your supervisor, it'll be a big blow to me. "
Vera was comforted by these words, and she smiled weakly.
She sighed silently in her heart at her own disappointment.
Even though she was more courageous than she was two years ago …
But is it still not enough?
…
Lu Zhou spent the entire day at the Princeton Institute for Advanced Study. He took the small gifts from his students and colleagues and returned home.
The gifts were not expensive. They were all small gifts that did not exceed 30 USD. However, it was the value that mattered.
As for the gifts he gave his students, they were fountain pens that he collected from conference sponsors when he attended academic conferences all over the world.
These gifts weren't expensive, but they were memorable.
After Lu Zhou put away the gifts, he sat on the sofa next to the fireplace. He closed his eyes and went into the system space.
He walked in front of the translucent holographic panel, and two lines of transparent text appeared in front of him.
[A. "Research on the even coherent state of a q-distorted harmonic oscillator in a finite-dimensional Hilbert space." Student: Wei Wen. Student Participation: 25%. Experience Type: Mathematics, Physics.]
[B. Collatz conjecture. Students: Vera, Qin Yue, Hadi. Student Participation: 70%. Experience Type: Mathematics.]
Before he went home, Vera uploaded the thesis to arXiv, which met the system's criteria. Therefore, the Collatz conjecture entry was also on the mission list.
Even though Lu Zhou didn't know how the system determined which students were his students, he had to admit that it was quite accurate.
Not just that, but it could even numerically calculate the proportion of their participation in the entire work.
"Is this a multiple-choice question?"
Lu Zhou looked at the two options on the screen. He crossed his arms in front of his chest and spoke to himself.
According to the system's mission description, he could choose a thesis to submit.
The total amount of experience points would be determined based on the academic value of the thesis, which would then be multiplied by the coefficient of student participation to calculate the final experience point.
Actually, from the design of the mission, it could be seen that the system wanted him to cultivate more genius students who could independently complete research work. Therefore, he was told to avoid direct participation in the mission.
In fact, Lu Zhou was trying to avoid doing this.
But now it seemed that even though he tried to avoid directly helping Vera, the system's evaluation of his contribution still reached 30%.
Because in the beginning, he formulated a clear research direction for them, as well as the framework of the entire research idea.
And it was precisely by following his train of thought that they completed the final proof.
Lu Zhou was hoping that the system would ignore this point, but it seemed like he was overthinking it.
"The system really doesn't give me any loopholes."
Lu Zhou looked at the translucent holographic panel and shook his head.
He didn't say anything else. He reached out his hand and selected "B". He then clicked the submit button in the dialog box that popped up.
Soon after, a light blue light swept across the holographic screen, and a line of dreamy words popped up.
You've already exceeded your reading limit for today. If you want to read more, please log in.
Login
Select text and click 'Report' to let us know about any bad translation.
