Having a car is really convenient and safe.

After a day of playing in Philadelphia and watching a movie, Lu Zhou and Chen Xuejie had dinner after a complete afternoon of relaxation, and then said goodbye and drove back to Princeton.

Parking the car in the parking lot near the Institute for Advanced Study, Lu Zhou, who was in a good mood, hummed a little song and went back to the historic apartment building and stepped on the stairs.

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

Glancing at Lu Zhou, she greeted in a mocking tone: "Went out to pick up girls?" ”

"I bought 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.

Once in the apartment, he left his coat and car keys on the couch, went to the kitchen to make himself a cup of coffee, and then returned to his desk to sit down and prepare to continue his work halfway through the morning.

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

[Master, there is a new mail!] OVO】

Did Professor Frank send it?

After receiving Xiao Ai's reminder, Lu Zhou opened the computer and logged in to the mailbox, only to find that there was not just one, but a total of two emails lying inside.

One of them had been in place for almost three days, probably when he was in retreat, and Xiao Ai may have reminded him again, but he just didn't notice.

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

[Dear Mr. Lu Zhou, I am Willa Puyuy who greeted you at Berkeley, I have some questions about the issues I discussed with you last time, I wonder if I can take up a little of your precious time?] 】

Pulyuy？

Although the spelling is in English, it probably sounds like Slav.

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 reserved.

Lu Zhou's brain made up for a long time, but he really couldn't associate that weak image and tone of speech with a bearded polar bear with a vogart in his hand.

It seems that it is still a stereotype......

Shaking his head, Lu Zhou put these inconsequential things aside, looked past the respectful wording and the adoration of himself between the lines, and looked directly at the main text.

【…… In the paper presented by Professor Hellfgot at the mid-year meeting of the Federal Mathematical Society, the equation J(n)=∫Φ(λ)· G（λ）²· H(λ)·e|-nλ|dλ, why can we directly lead to the conclusion in proposition (2.1)? 】

Seeing this, Lu Zhou's eyebrows raised slightly.

Yo, the perception is quite high.

Sure enough, IMO's gold medal is indeed a cut above the average person in terms of mathematical talent.

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

Lu Zhou smiled, and the editor replied.

[Because we have to use the circular method to deal with intervals and establish several equidistribution results, we have to pave the way for our theory.] So we note that S1(q,α)=∑e(αm³/q), C1(q,α)=∑e(αm³/q²), and bring in Td(n,q)=∑S1(q,αd³)·|C1（q，αd³）|· e(-an/q)/qψ²(q)...... Then, what do we get? Think for yourself. 】

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

At the end of the email, he didn't tell Vera directly what she could get out of these processes, he preferred that she would 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.

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

Taking a sip of coffee, feeling the bitter taste spreading from the tip of his tongue, Lu Zhou suddenly realized that he seemed to have forgotten to put sugar.

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

"So fast?"

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

The text has only one line of words.

【…… Can we get the absolute convergence of series δd(n)=∑Td(n,q)? 】

Seeing this, the corners of Lu Zhou's mouth hooked up a smile, and he nodded with satisfaction.

The children can be taught!

Sure enough, he didn't look away, and he was indeed a promising student.

Although he may have a little less experience, he understands very quickly and has a keen instinct for numbers.

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

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

[Correct solution.] 】

It didn't take him about a minute before he received a reply.

[Thank you.] 】

Well, and it's very polite.

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

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

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

series δd(n) = ∑Td(n,q) absolute convergence......

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

Suddenly thinking of something, Lu Zhou quickly opened his computer's collection, flipped out the paper that Helfgot submitted to the year-end meeting of the Federal Mathematical Society, found the position of the third line of 11 pages, and looked down one line at a time.

The wall clock on the wall ticked and ticked, and before you knew it, the hour hand was halfway through.

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, Helfgot is undoubtedly a master in the field of analytic number theory, just like Chen Jingrun is to the sieve method.

Even Helfgot himself had no expectations that the circle method would prove Goldbach's conjecture, and Lu Zhou did not expect to dig out the blind spots that he had overlooked from under the master's nose.

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

Because the old gentleman's paper was too jumpy, and many conclusions were too obvious, Lu Zhou didn't think deeply, if it weren't for Vera reading the paper too carefully, and she happened to not understand here, he almost missed this discovery.

For this unexpected surprise, Lu Zhou was excited.

Although this discovery does not directly solve the ultimate proposition of Goldbach's conjecture, it can improve his tool!

Let his group construction method return to the Goldbach conjecture......

Probably?

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

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

The train of thought was interrupted.

It's just a little bit close!

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

The eyes that wandered around because of letting their thoughts wander somehow fell on the computer screen.

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

As soon as he thought of this, he immediately sat up.

Silently saying sorry to Professor Frank in his heart, Lu Zhou clicked on the email that he had almost forgotten about.

The body of the message is short.

It's so short that it's only one line.

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