Having a car was indeed convenient and safe.
Lu Zhou spent the whole day in Philadelphia and even watched a movie. After that, he had a relaxing afternoon with Chen Yushan. After dinner, they said their goodbyes and drove back to Princeton.
He parked his car in the parking lot near the Institute for Advanced Study. Lu Zhou was in a good mood as he hummed a song and walked back to the historic apartment building. He then walked up the stairs.
When he walked to the second floor, Molina, who was wearing sportswear, came out of her room with a garbage bag. It seemed like she was going for a jog.
She looked at Lu Zhou and said in a joking tone, "Going out to pick up girls?"
"I went to buy a car."
Lu Zhou shook the car keys on his index finger and didn't say anything else. He turned around and went back to his room.
After he entered his apartment, he threw his jacket and car keys on the sofa. He first went to the kitchen and made himself a cup of coffee. He then returned to his desk and sat down. He was ready to continue his morning work.
Suddenly, a message from Xiao Ai popped up on his phone screen.
[Master, you have mail! OVO]
Is it from Professor Frank?
After receiving a notification from Xiao Ai, Lu Zhou opened his computer and logged into his email. He found out that there was more than one email. There were two emails in total.
One of them had been there for almost three days. It was probably sent when he was on a retreat. Maybe Xiao Ai reminded him, but he didn't notice.
Because the address was a bit unfamiliar, Lu Zhou was afraid that he would miss something, so he opened the email first.
[Dear Mr. Lu Zhou, I am Vera Pulyuy from Berkeley. I have some questions about the issues we discussed last time. I don't know if I can take up some of your precious time?]
Pulyuy？
Even though it was spelled in English, it sounded like Slavs.
However, judging from the wording of the letter, this little girl was too polite. He was not a famous professor, so there was no need for her to be so formal.
Lu Zhou's imagination ran wild for a long time, but he really couldn't connect that weak image and tone with a bearded polar bear holding a vodka.
Looks like it's still an old impression …
Shaking his head, Lu Zhou put these unimportant things aside. He skipped over the respectful wording and the worship in the words and directly looked at the main body.
[… In the paper presented by Professor Helfgott at the mid-year conference of the Federal Mathematical Society, the third page of the 11-line formula J (n) = Φφ (λ) · G (λ) 2 · H (λ) · e | -nλ | dλ. Why can the conclusion in proposition (2.1) be directly derived?]
Lu Zhou raised his brows slightly.
Yo, his comprehension is quite high.
As expected of the IMO gold medalist, his talent in mathematics was indeed higher than the average person's.
At least compared to the conceptual problem she asked him about closed-orbit integrals and the residue theorem, this problem was closer to the core part of the circle method.
Lu Zhou smiled and replied to the email.
[Because we have to use the circle method to deal with the interval and establish several equal distribution results, we must pave the way for our theory. So we put the formula into the circle method … Then, what do we get? Think about it yourself.]
After checking the email from beginning to end and confirming that there were no major problems, Lu Zhou clicked send.
At the end of the email, he did not directly tell Vera what she would get from this process. He wanted her to find out through her own thinking.
If she wanted to develop in the direction of mathematics in the future, she would have to go through this process, whether it was in the direction of number theory or other directions.
Elementary mathematics knowledge could be obtained through training, but higher level knowledge had to be sublimated through thinking. This was because no one could give a standard answer.
Lu Zhou took a sip of coffee and tasted the bitterness on the tip of his tongue. He suddenly realized that he forgot to add sugar.
He went to the kitchen to get some sugar. When he returned to his desk, he suddenly saw that he had received a reply.
"Already?"
Lu Zhou put down his coffee cup and opened the email with a surprised expression.
There was only one line of text.
[… Can you get the absolute convergence of the series δ d (n) = ∑ Td (n, q)?]
Lu Zhou smirked and nodded with satisfaction.
She's worth teaching!
I didn't make a mistake, she is a promising student.
Even though she doesn't have much experience, her comprehension ability was very fast and her intuition for numbers was quite sharp.
If he were a professor at Berkeley, he would not mind taking her as his student.
Lu Zhou smiled as he typed an email and clicked send.
[Correct.]
In less than a minute, he received a reply.
[Thank you.]
Yeah, she's also very polite.
Lu Zhou closed the email and looked at the calculations that he had written in the document on his desk. He was about to throw it into the recycle bin.
However, at this moment, he suddenly exclaimed softly. He stared at the lines of calculations and fell into deep thought.
The absolute convergence of the series δ d (n) = ∑ Td (n, q) …
From here on, I can introduce the circle method and solve proposition (2.1).
Lu Zhou suddenly remembered something, and he quickly opened his computer's collection. He found Helfgott's thesis submitted to the Federal Mathematics Society's end-of-year conference, found the third line, page 11, and began to read it.
The clock on the wall ticked away, and before he knew it, the hour hand had already passed half a second.
Suddenly, Lu Zhou seemed to have figured something out. He quickly picked up a pen and began to calculate on the paper.
Helfgott was undoubtedly a master in the field of analytic number theory, just like Chen Jingrun was a master in sieve method.
Even Helfgott himself did not have any expectations of using the circle method to solve Goldbach's conjecture. Lu Zhou did not expect to be able to dig out Helfgott's blind spots from under his nose.
However, when he was reviewing the thesis, he vaguely noticed a detail that he did not notice before.
Because the old man's thesis was too jumpy and there were many obvious conclusions, Lu Zhou did not think too deeply about it. If it were not for the fact that Vera read the thesis too carefully, he would have missed this discovery.
Lu Zhou was excited about this unexpected surprise.
Although this discovery could not directly solve Goldbach's conjecture, it could improve his tool!
Let his Group Structure Method return to Goldbach's conjecture …
Probably?
The tip of the pen that was moving quickly on the paper gradually slowed down and finally stopped.
Lu Zhou looked at the four pages in front of him and the fifth page that he could not continue. He threw away the pen in his hand and scratched his head in annoyance.
My train of thought is interrupted.
I'm so close!
The clock ticked away, and the night outside the window gradually darkened.
Because he had allowed his thoughts to wander, his eyes somehow landed on the computer screen.
Suddenly, Lu Zhou noticed that he still had an email that he had not read.
Thinking of this, he immediately sat up.
Lu Zhou apologized to Professor Frank in his heart. He then opened the email that he had almost forgotten about.
The email was very short.
It was only one line.
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