Chapter 388: Proof of Kakutani conjecture

Hearing that compliment, Vera's mouth twitched a happy arc.
For her, this is undoubtedly the best compliment in the world.
Standing beside Lu Zhou, she said softly.
"Your guess is correct. Kakutani's conjecture is a number theory problem and a complex analysis problem ..."
As early as 1994, g and ardus proved that the 3n + 1 conjecture is equivalent to the functional equation h = h + / 3z). The analytical function solution in the unit disk is in the form h = h0 + h1z /.
On this basis, Schleicher et al. Also proved in 1998 that any whole function h makes g = z / 2 + / 2 + 1 / πsinπz + hsin2πz satisfy: NΦ.
Based on these two conclusions, Vera constructed a clever transcendental entire function and proved that there is an entire function h, so that for each branch D of g and Φ in the above conclusion containing a positive integer, z0 ∈ D exists. Make ∞ / k = 1 converge to 1.
It is not difficult to launch from this, Kakutani conjecture is established!
"Very good proof ..." Lu Zhou said with a reassuring smile on his face, "I was surprised by the excellentness."
From the summer of 16 years, it is now the end of 17 years.
He was glad to see that his students had grown up.
I am also glad to see that the "group construction" theory that I have built for the problem of additive number theory does not stop at Goldbach's conjecture. Not only that, but also the inheritance of my students.
He now has some experience, what kind of feeling is the "delight" depicted by the system.
"... Thanks for your guidance." Vera said humbly, her eyes full of gratitude.
Although she completed the process, the whole proof of thought was provided by Lu Zhou.
From her staged achievements at the Berkeley report at the beginning of the year to the present and working with Qin Yue and Hardy to complete the final certification, all work revolves around this idea.
Going all the way to the end, she knows more than anyone how important these obscure tasks are.
Lu Zhou smiled: "You don't have to be humble, all I provide is direction, and it's you who runs to the finish."
After a pause, he continued: "... I suggest you submit your paper on this paper, but the editors are on vacation these days. You can hang the paper on Ariv ... maybe, Editor will give you the rest of your vacation. "
Hanging a paper on Ariv as a preprint can play a role in pitting, but it doesn't matter if it is not hanging. Kakutani guessed that it was very popular in the 80s and 90s, but it is not a popular research direction until now. The chance of a crater is almost zero.
The reason for this suggestion, of course, Lu Zhou also has a little selfishness in it.
According to the inference he made while solving Goldbach's conjecture, the system's principle of determining task completion is based on the time when the paper was published.
So as long as the paper is hung on Ariv, the task can be considered completed.
After listening to Lu Zhou's words, Willa nodded seriously.
"I see. I'll do it right away."
Lu Zhou smiled: "That's it. As for the formula on the blackboard, I'll wipe it off for you ... Thank you for your gift."
Hearing the praise, Vera's face showed a happy smile.
After a while, she bowed her head suddenly, her cheeks flushing slightly.
"professor."
Lu Zhou: "What's wrong?"
With courage in her heart, she looked up and looked at Lu Zhou.
"Can I ... make a wish to you?"
"I'm not Santa Claus. I may not be able to put what you want in the socks of your bedside table." I can do it, and I will definitely help you. "
"I……"
Willa just opened her mouth.
But at this moment, she suddenly realized that her own mind might cause trouble to him.
When I almost reached my lips, I couldn't explain it somehow.
"I ... want to read your doctorate."
Slightly hesitated, Lu Zhou smiled immediately, "Welcome! Rather, if you suddenly want to change to a mentor, you will be hit hard."
Getting a little comfort from this sentence, Vera smiled weakly.
For her indifference, she sighed silently in her heart.
Although now I have more courage than two years ago ...
But is it still not enough?
...
After playing all day at the Institute for Advanced Studies in Princeton, Lu Zhou returned home with a small gift from his students and colleagues.
Gifts are not expensive. They are small gifts that do not exceed 30 US dollars, but they are worthless and valuable.
As for what he gave to the students, it was the pens he collected from the conference sponsors when he attended the conference around the world.
These gifts are not too precious, but they are full of commemorative significance.
After placing these gifts, Lu Zhou sat on the sofa near the fireplace, closed his eyes and meditated on the system, sinking his consciousness into the system space.
Walking to the translucent holographic panel, two lines of transparent text appeared in front of him.
Before he returned home, Willa uploaded the paper that had already been sorted out and uploaded it to Ariv, which met the conditions for system judgment. Therefore, entries about Kakutani's conjecture are also listed on the task list.
Although I don't know how the system judges who is their student, I have to say that it judges it quite accurately.
Not only that, it can even calculate their proportion of participation in the entire work numerically.
"Is this a multiple choice question?"
Looking at the two options on the screen, Lu Zhou with his arms around his chest, said to himself thoughtfully.
According to the system's description of the task, he can choose a paper to submit the task.
The total reward experience is determined according to the academic value of the propositions contained in the project, and then multiplied by the coefficient of student participation to calculate the final experience value.
In fact, it can be seen from the design of the task that the system hopes that he can train more academic fighters who can independently complete the research work. Therefore, he is required to try to avoid directly participating in the topic in the task ~ There are also avoidances.
However, it now seems that even if he tried to avoid directly helping Willa them, the system judged his contribution to 30%.
Because at the beginning, he formulated a clear research direction for them, as well as the framework of the entire research idea.
And they also followed his thinking to complete the final proof.
Lu Zhou had a little expectation that the system might ignore this, but now it seems that she is thinking too much.
"It's really nothing for me to drill."
Looking at the translucent holographic panel, Lu Zhou shook his head helplessly.
He didn't say anything anymore, he reached out and selected "B", and in the dialog box that popped up later, he clicked the confirm submission button.
Soon, a pale blue light swept across the holographic screen, and a line of large characters popped like a dream.