The Princeton campus.
It was the coldest time of the year in New Jersey, and there were snowflakes outside the window. The accumulated snow piled up on the windows and roofs, turning the Oxford-style campus that was immersed in an academic atmosphere into a fairytale castle.
Vera sat quietly in the library activity room of this "castle". She quietly sat at the desk and looked at the computer. The bookshelf next to her and the snow outside the window looked like a painting.
Her light golden long hair hung down gently. Although her fair skin revealed a paleness that made people feel uneasy, the gentleness and determination in her sapphire-like eyes gave people a sense of security. It also added a bit of dazzling color to her.
On the computer screen was Lu Zhou's reply.
His concise language style and his direct use of words were very characteristic of him.
[I've read your email.
[The method of using the irreducible unitary representation theory of the octonion Heisenberg group and doing a Fourier transform on it is indeed a very interesting improvement idea.]
[This also reminds me of a quantitative version of the weak form of the Riemann conjecture proved by Professor Levinson and Professor Montgomery in 1974. The number of zeros of ζ (s) in the open region {-1 < Re (s) < 1/2, T1 < Im (s) < T2} and ζ (s) in {0 < Re (s) < 1/2}.
The ratio of the zeros in T1 < Im (s) < T2} is gradually approaching 1 … A similar method was used.
[Very good. The idea you proposed just happened to indirectly answer a question that I've had for a long time. Do you remember what I said a long time ago? The Riemann conjecture is an analytic number theory problem, but it is still a complex analysis problem. We have to solve it the same way we solve complex analysis problems, but we can't just limit ourselves to that.
[My suggestion is to start with the Plancherel formula on a class of simply connected nilpotent Lie groups G _ n and discuss the sub-elliptic properties of the left invariant differential operators on G _ n. We should be able to find something unexpected.
[By the way, I suggest that you sort out the things in the email and send it to me. That way, it'll be easier for me to use it.]
"Isn't it limited to complex analysis? Your style really hasn't changed at all. "
After reading the email from the beginning to the end, Vera's mouth curved into a smile.
But then the curvature of her lips gradually flattened. The little girl sitting at the desk frowned and pondered for a long time. She reached out and picked up the ballpoint pen in the pen holder. She wrote down the ideas proposed by Lu Zhou on the draft paper.
At the same time, he also integrated some of his own thoughts into it.
At this time, the door of the activity room was suddenly pushed open, and a woman in a large windbreaker walked in quickly.
Molina shook off the snow on her body and hung her coat on the hanger at the door. She took two sandwiches and coffee and walked next to Vera.
"Don't look at the computer. Eat your lunch first. I brought you your favorite tuna fish sandwich … and peppermint coffee. What kind of weird taste is this? I can't believe someone would put peppermints in their coffee, and it's even weirder that someone would buy them. "
"Thank you, Molina." Vera warmed her hands with the hot coffee and gave Molina a gentle smile. She said, "But this isn't putting peppermints in coffee. It's soaking the coffee in peppermint leaves, waiting for five minutes … Just like making tea. "
"I can't stand the weird smell … What are you looking at?"
"Professor Lu's reply." Vera blushed and covered her mouth with a piece of paper. She then said, "A few days ago, I was researching his hyperelliptic curve analysis thesis. I thought of an application of the irreducible unitary representation theory of the Heisenberg group of octonions, so I tried to research it … It seems like my research came in handy."
Molina looked at the email on her screen and spoke with a sullen tone.
"Hey, you're colluding with the enemy! Don't tell me you forgot that I'm your comrade. "
"Professor Lu isn't our enemy." Vera looked at Molina and showed her brave side. She said in a serious tone, "We agreed on this from the beginning, why can't we solve this problem together? Solving the Riemann conjecture isn't something that can be done by one person. "
Molina looked at Vera's stubborn face and opened her mouth, but she couldn't say a word.
She admitted that she had her own selfish motives, but who didn't?
If Lu Zhou was the one who proved the Riemann conjecture, even if no one said it, everyone would give him all the credit and think that he solved 99% of the problem.
Just like who would remember Hardy's collaborator? Who would remember which year Hilbert worked with someone to complete an important thesis or a major research result?
Unless it was a problem that Hardy and Hilbert worked together to solve.
In a situation where there was a huge gap between the two sides, people tended to remember the most memorable name and forget the insignificant one.
She admitted that mathematics was her life, and she only researched mathematics because she liked it. However, it was also one of her unshirkable responsibilities to revive the Abel family.
At least, that was what she thought.
However, looking at Vera who was not backing down, she could not say anything selfish.
"… I really don't know what to do with you." Molina sighed and scratched the back of her head. She said, "If you think things are that simple, then just continue on the right path."
"Thank you," said Vera with a gentle smile and sincerely expressed her gratitude.
"You're welcome … Speaking of which, is your body really okay?" Molina looked at the trash can next to her and said worriedly, "You were coughing all day yesterday, and you don't seem to be in a good state today."
Vera gently shook her head and smiled as she said, "Actually, I'm fine, don't worry about me."
Molina hesitated for a bit before she said, "How about I go to the 45-minute report in St. Petersburg for you? You should rest here for a bit."
"No, I will definitely go myself." Vera blushed and shook her head. She said, "He must be looking forward to my report, I won't let him down."
Molina took a deep breath and finally asked the question she wanted to ask for a long time, "Can I ask, what kind of illness do you have?"
Vera's fingers that were holding the pen paused. She shook her head and spoke with a gentle smile.
"You don't have to worry about me, I'm fine."
Even though she said this, her voice didn't make Lu Zhou feel at ease.
Molina looked at Vera and felt her heart beat faster.
She impulsively grabbed the draft paper and pen from Vera's hand. She pressed down on Vera's slender shoulder and spoke with an unquestionable voice.
"Listen, you need to rest! Patients should stay in bed obediently. Look at you — "
"I don't need it, give it to me …" Vera grabbed the draft paper and pen from Molina's hand and stubbornly said, "I don't need rest. Trust me, I know what I need."
There's not much time left …
There's no time to waste.
Molina looked at the unyielding girl and finally made a compromise. She let go of Vera's shoulder and spoke in despair.
"I'm impressed!"
She turned around and walked to the door. She grabbed her wet coat and put it on herself. She then walked out of the activity room.
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