Chapter 232 Ideas Emerge!

Having a car is really convenient and safe.

After spending a day in Philadelphia and watching a movie, Lu Zhou had a relaxing afternoon and had dinner with Senior Sister Chen. Then he said goodbye and drove back to Princeton.

After parking the car in the parking lot next to the Institute for Advanced Study, Lu Zhou hummed a little song in a good mood and went back to the apartment building full of history and stepped up the stairs.

When he walked up to the second floor, Molina, who happened to be wearing a sportswear, came out of the room with a garbage bag, apparently ready to go for a jog.

Glancing at Lu Zhou, she greeted in a teasing tone: "Going out to pick up girls?"

"Going to buy a car."

Shaking the car key on his index finger, Lu Zhou didn't talk nonsense with her, turned around and went back to his room.

After entering the single-person apartment, he threw his coat and car keys on the sofa, first went to the kitchen to make himself a cup of coffee, then returned to his desk and sat down, ready to continue his half-morning work.

At this moment, a message from Xiao Ai popped up on his mobile phone screen.

[Master, there is new mail! OVO】

Did it come from Professor Frank?

After receiving Xiao Ai's reminder, Lu Zhou turned on the computer and logged into the mailbox, only to find that there were not just one, but two emails lying in it.

One of them has been posted for almost three days, and it was probably sent when he was in retreat. Maybe Xiao Ai reminded him again, but he just didn't notice it.

Because the sending address was a bit unfamiliar, Lu Zhou, who was afraid of delaying something, clicked on the email first.

[Dear Mr. Lu Zhou, I am Greetings from Vera Puyui at Berkeley. I have some questions about the issues I discussed with you last time. Can I take up a little of your precious time? 】

Pulyuy?

Although the spelling is English, but judging from the pronunciation, it is probably Slavic.

However, judging from the wording of the letter, this little girl is too polite, and he is not a well-known professor, so there is no need to be so cautious.

Lu Zhou thought about it for a long time, but he really couldn't connect that weak image and tone of voice with a polar bear with a big beard and a vodka in his hand.

It seems that the inherent impression is still causing trouble...

Shaking his head, Lu Zhou put these irrelevant things aside, skipped those humble words and the admiration for himself between the lines, and looked directly at the main text.

[...In the paper presented by Professor Helfgott at the mid-year meeting of the Federal Mathematical Society, the 11-line formula on page 3 J(n)=∫Φ(λ)·G(λ)·H(λ)· e|-nλ|dλ, why can the conclusion in the thesis proposition (2.1) be drawn directly? 】

Seeing this, Lu Zhou raised his eyebrows slightly.

Yo, your comprehension is quite high.

Sure enough, the IMO gold medal, the talent in mathematics is indeed higher than the average person.

At least compared to the conceptual question about closed-orbit integrals and residue theorem she asked herself last time, this question is close to the core part of the circle method.

Lu Zhou smiled and edited the email reply.

[Because we want to use the circle method to deal with intervals and establish several equidistributed results, it is necessary to pave the way for our theory. So we record S1(q, α)=∑e(αm/q), C1(q, α)=∑e(αm/q), and bring it into Td(n, q)=∑S1(q, αd) ·|C1(q, αd)|·e(-an/q)/qψ(q)... Then, what can we get? Think for yourself. 】

After checking it from beginning to end, after confirming that there were no major problems, Lu Zhou clicked send.

At the end of the email, he didn't directly tell Vera what can be gained through these processes, and he hoped that she could find out through her own thinking.

If she plans to develop in the direction of mathematics in the future, whether she chooses the direction of number theory or other directions, this process must be experienced.

The knowledge of elementary mathematics can be obtained through training, but higher-level knowledge must be sublimated in thinking, because no one can give a standard answer.

Picking up the coffee and taking a sip, feeling the bitter taste spreading from the tip of his tongue, Lu Zhou suddenly realized that he seemed to have forgotten to add sugar.

He went to the kitchen to get sugar, and when he returned to the desk, he suddenly found that he had received a reply.

"So fast?"

Putting down the coffee cup, Lu Zhou opened the email with a surprised expression.

The text is only one line.

[...Can the series δd(n)=∑Td(n,q) be absolutely convergent? 】

Seeing this, a smile appeared on the corner of Lu Zhou's mouth, and he nodded with satisfaction.

Children can be taught!

Sure enough, he was right, he was indeed a promising student.

Although he may be a little less experienced, his comprehension ability is very fast, and his intuition for numbers is also quite keen.

If he were a professor at Berkeley, he wouldn't mind taking her as his apprentice.

Lu Zhou edited an email with a smile and clicked send.

【correct. 】

After about a minute, he received a reply.

【thanks. 】

Well, and very polite.

After closing the email, Lu Zhou looked at the formulas he had edited in the document on the side of the desktop, and was about to fork it and drag it into the recycle bin.

However, at this moment, he suddenly let out a sigh, staring at the line of calculations, and fell into deep thought.

Td(n,q)=∑S1(q,αd)|C1(q,αd)|·e(-an/q)/qψ(q)...

The series δd(n)=∑Td(n, q) absolutely converges...

From here, the circle method can be introduced to solve the proposition (2.1).

Suddenly thought of something, Lu Zhou quickly opened his computer collection, turned out the paper that Helfgott submitted to the year-end meeting of the Federal Mathematical Society, found the position of the third line of page 11, and read down the line down.

The wall clock on the wall was ticking, and before I knew it, the hour hand had passed half a frame.

Suddenly, Lu Zhou seemed to have figured out something, quickly picked up the pen, and quickly calculated on the paper.

For the use of the circle method, Helfgott is undoubtedly a master in the field of analytical number theory, just like Chen Jingrun is in the sieve method.

Even Helfgott himself has no expectations for the method to prove Goldbach's conjecture, and Lu Zhou does not expect to dig out the blind spots that he has ignored under the nose of the master.

But when he was reviewing this paper just now, he vaguely discovered a detail that he hadn't noticed before.

Because the old man's thesis is too jumpy, and there are many overly obvious conclusions, Lu Zhou didn't think about it in depth. If it wasn't for Vera who read the paper too carefully, and just didn't understand it, he almost got along with this one. Found passing by.

For this unexpected surprise, Lu Zhou was very excited.

Although this discovery cannot directly solve the ultimate proposition of Goldbach's conjecture, it can perfect his tools!

Let his group construction method return to Goldbach's conjecture...

perhaps?

The tip of the pen that was shaking rapidly on the paper gradually slowed down and finally stopped.

Looking at the completed four pages in front of him, and the fifth page that could not be continued, Lu Zhou dropped the pen in his hand and scratched his hair a little irritably.

The train of thought was interrupted.

It's just a little bit closer!

The clock is ticking, and the night outside the window is getting darker.

His eyes wandering around because he let his thoughts spread, somehow landed on the computer screen.

At this time, Lu Zhou suddenly noticed that he seemed to have an email that he hadn't read.

Thinking of this, he immediately sat up.

Silently saying sorry to Professor Frank in his heart, Lu Zhou opened the email that he almost forgot.

The body of the message is very short.

As short as one line.

[About the 750GeV signal, I need to talk to you face to face... When do you have time? 】