Scholar's Advanced Technological System - Chapter 231

Chapter 231: Ideas Emerge!

It really was convenient and safe to have a car.

Lu Zhou spent the whole day in Philadelphia with Chen Yushan. They watched a movie, chilled around and had dinner. After that, Lu Zhou drove back to Princeton.

Lu Zhou parked the car near the Institute of Higher Education. He was in a good mood and he started humming while walking up to his apartment.

When he walked up to the second floor, he saw Molina in sports clothes. It looked like she was about to go running.

Molina looked at Lu Zhou and asked, “Went on a date?”

“Bought a car.”

Lu Zhou shook the car keys and did not say much to her as he went straight into his apartment.

Once he was inside, he threw his jacket and car keys on the sofa. First, he went to the kitchen and made himself some coffee. He then sat down at his desk and was ready to continue working.

Suddenly, a message from Xiao Ai popped up on his phone screen.

[Master, new mail!]

Is it from Professor Frank?

Lu Zhou opened his computer and logged into his email. He did not just see one, but two emails in his inbox.

One email was sent three days ago, probably when he was still locked in his room. He probably did not see Xiao Ai’s notification.

Lu Zhou did not recognize the sender’s email address. Since he was afraid that he missed something important, he opened this one first.

[Mr. Lu Zhou, I am Vera Pulyuy from Berkeley. I have some questions from our last discussion. Don’t know if I can take up some of your precious time?]

Pulyuy?

Probably a Slav name?

Why is this girl so polite? It’s not like I’m some famous professor.

Lu Zhou scratched his head. He could not imagine this little girl being from a country with bearded large men and polar bears.

Never would’ve thought she is a Slav…

Lu Zhou shook his head and put these insignificant things aside. He skipped the paragraph worshiping him and looked at the important part of the email.

[… In the paper reported by Professor Helfgott at the mid-year conference of the Federal Mathematical Society, the third page of the 11-line formula J(n)=∫Φ(λ)·G(λ)2·H(λ) ·e|-nλ|dλ. Why does it directly draw the conclusions in the thesis proposition (2.1)?

Lu Zhou lifted his eyebrows.

Oh, she knows what she’s talking about.

No wonder she’s an IMO gold medalist, she’s quite talented.

Compared to the question she asked me last time, this question was at least related to the circle method.

Lu Zhou smiled and typed a response.

[Because we have to deal with the interval using the circle method and establish several equal distribution results. So we record S1(q,α)=∑e(αm3/q), C1(q,α)=∑e(αm3/q2), brought into Td(n,q)=∑S1(q,αd3) ·|C1(q,αd3)|·e(-an/q)/qψ2(q)…and then, what do we get? Think about it yourself.]

Lu Zhou double checked his email and once he made sure there were no mistakes, he sent it out.

In the email, he did not directly answer Vera. He hoped that she could figure it out on her own.

If she wanted to study mathematics in the future, whether it was number theory or another field, this process of figuring it out on her own was crucial.

Basic mathematics could be taught, but higher levels of mathematics must be digested by herself. This was because everyone had different interpretations, so there was no standard answer.

Lu Zhou took a sip of his bitter coffee before he realized that he forgot to add sugar.

He walked to his kitchen and got some sugar. When he returned to his desk, he found out that he already received a reply.

“That quick?”

Lu Zhou placed down the coffee and opened the email.

The body had only one line.

[… can you get the order δd(n)=∑Td(n,q) absolute convergence?]

Lu Zhou smirked as he nodded with satisfaction.

This girl is worthy to be taught!

As he estimated, this student had potential.

Although her experience was low, her ability to understand and intuition toward numbers was high.

If he were a professor at Berkeley, he definitely would not mind being her supervisor.

Lu Zhou smiled and wrote a reply.

[Correct.]

Within a minute, he received a reply.

[Thank you.]

Wow, she’s very polite as well.

Lu Zhou closed the email and looked at the calculations he did on the computer. He was about to delete this document when he suddenly stared at the lines of calculations. He then went into deep thought.

Td(n,q)=∑S1(q,αd3)·|C1(q,αd3)|·e(-an/q)/qψ2(q)…

The series δd(n)=∑Td(n,q) is absolutely convergent…

From here on, I can introduce the circle method and solve the proposition (2.1).

Lu Zhou suddenly realized something. He quickly opened his computer files and found Helfgott’s thesis that was submitted to the Federal Mathematics Society’s conference. He found the third line on page 11 and started to read.

The clock on the wall slowly ticked. Without him knowing, it had been half an hour.

Suddenly, Lu Zhou realized something. He quickly picked up a pen and started writing on paper.

Helfgott was undoubtedly the master of the circle method, just like how Chen Jingrun was the master of the sieve theory.

However, even Helfgott himself did not expect that the circle method could be used to solve Goldbach’s conjecture. Lu Zhou had not expected himself to defeat the master while he was looking for a possible way.

However, when he was reviewing the thesis, he found a detail that he did not notice before.

The old man’s thesis was very long, and thus, Lu Zhou did not examine it carefully. If it was not for Vera, Lu Zhou would not have noticed this detail.

Lu Zhou was ecstatic at this unexpected surprise.

Although this discovery could not solve Goldbach’s conjecture, it would perfect his tools!

It could possibly let him apply his Group Structure Method to Goldbach’s conjecture…

… Maybe?

His pen slowed down and stopped.

As Lu Zhou looked at the four pages in front of him, he could not continue to write.

He had lost his train of thought.

I was so close!

The clock kept ticking away and the sky outside the window gradually darkened.

Lu Zhou looked at his computer screen.

Suddenly, he realized that he had another un-read email.

He immediately sat up straight.