Chapter 107 The final step to prove the Weyl-Berry conjecture
In the auditorium, Xu Chuan was a little surprised when he heard the invitation from Tao Zhexuan.
After all, the gap between the two is too big.
Terence Tao is 41 years old this year and has already won various top mathematics awards such as the Fields Medal, Clay Research Award, MacArthur Award, Waterman Award, and Breakthrough Prize in Mathematics.
In addition, he is also an academician of the Royal Society, a foreign academician of the National Academy of Sciences, an academician of the American Academy of Arts and Sciences, and a national academician of Australia.
And now, he is just a college student who has proved the guess of world-class difficulty.
The gap in status between the two is really too big.
Of course, mathematics doesn't pay much attention to these things. In the world of mathematics, strength is respected. As long as you are truly capable, not to mention college students, even high school and junior high school students can gain the respect of others.
As for the invitation, Xu Chuan's heart was only moderately excited.
Although Professor Terence Tao is a Fields Medal winner, Princeton has more Fields Medal winners. Although the University of California is very good and can be said to be one of the top three in the United States after Puhayer, in comparison
Next, Princeton is undoubtedly stronger.
So he declined Professor Tao's invitation directly.
Hearing Xu Chuan's rejection, Tao Zhexuan felt regretful, but he also knew that the most suitable school for the young man in front of him was not the University of California, Berkeley, but the one at their feet.
When it comes to mathematics alone, Princeton can beat all other universities in the United States.
...
After listening to Professor Schultz's lecture, Xu Chuan also returned to his hotel room.
After making a call and asking the hotel waiter to deliver a dinner, he took out his notebook and pen from his schoolbag and began to sort out today's gains.
Whether it was the 'p·s progressive-geometric theory' explained by Professor Schultz at the lecture, or the exchange between the two when he met Professor Terence Terence by chance, they all brought him a lot of feelings and mathematical knowledge.
Now that the memory is clearest in his mind, writing down these things again will help deepen his understanding of this knowledge.
"The main conjecture of Iwasawa theory is: ch(a)= ch(e/c), a is an ideal group in the number field, and is a purely algebraic object. The cyclotomic unit is essentially an analytical object."
"In fact, let ζ(p, s)=ζ(s)·(1? p?s)=∑p|n*1/n^s, this function is called the p-adic ζ function, which is zp
A continuous function, and its value at negative integers can be represented by the interpolation of a leading polynomial of zp[t]..."
"...."
Sorting through the gains in his mind, Xu Chuan thought over and over whether these gains could be applied to certain aspects.
This is his unique habit.
It is true that mathematics requires inspiration, but inspiration is based on knowledge reserves.
There is a saying that "Opportunities only come to those who are prepared." If you are not prepared, you will not be able to catch inspiration when it comes.
"Take a suitable Garrod field as a finite commutative group and equate the algebraic objects with p-adics..."
When the black pen in his hand recorded a string of characters on the white notebook, a flash of lightning flashed in Xu Chuan's mind.
"Wait... The elements of the Garois field can be generated by the primitive polynomial on the field. The additive unit of the field obtained by the primitive polynomial is 0, and the multiplicative unit is 1.
, the primitive polynomial is a prime polynomial.”
"Although it is a finite field, the Dirichlet field can be expanded to infinity. Is it possible to construct a domain value through the expansion of the number field, and then move it to high latitudes, and then use the Dirichlet field to solve the problem of Ω
Are the fractal dimensions and spectrum of fractal measures limited?”
"The final requirement of the Weyl-berry conjecture is to prove that it is a spectral invariant of any fractal dimension and fractal measure. If the boundary points can be given, then the fractal dimension of Ω and the spectrum of the fractal measure should be determined."
"This idea was indeed my initial inspiration, but I didn't have enough basic knowledge for me to check it. Now it seems that this inspiration is still a little flawed, but it doesn't matter, I can try it first."
Staring at the information recorded on the manuscript paper, Xu Chuan fell into deep thought.
When he had a cold last year, he got the inspiration to prove the Weyl-berry conjecture, but at that time he was unable to check it because he did not have enough basic mathematics.
Today, after listening to Professor Schultz’s lecture on ‘p·s progressive domain-geometric theory’ and the discussion with Professor Terence Tao, this opportunity seems to have arrived.
After realizing this, Xu Chuan got up and picked up the landline phone beside the bed and called the waiter in the lobby on the first floor and asked them to send a stack of manuscript paper or printing paper.
This is a free service that must be provided by any hotel in Princeton.
Because this is the holy land of mathematics, no one knows whether a mathematician stayed in the hotel or suddenly had inspiration one night.
Therefore, for the sake of academics, Princeton has done its best in all services.
Soon, the hotel waiter brought over a thick plate of manuscript paper, along with a blessing.
"Good luck to you, sir."
However, Xu Chuan ignored it. He was still immersed in the idea in his mind. He took the manuscript paper from his brother's hand and closed the door with a bang.
The guy at the door didn't mind. Working here, he has seen too many mathematicians and many 'weirdos'.
The customer in this room couldn't even be called strange. He didn't pay attention to him. It only meant that he was immersed in thinking about a certain problem at the moment.
Although he looks younger and doesn't look like a mathematician, there are still young mathematicians.
For example, Professor Terence Teru stayed at their hotel more than ten years ago, and that expert even solved a mathematical conjecture in their hotel.
This chapter is not over yet, please click on the next page to continue reading! The room at the back is reserved as a room of special significance and is rarely open to the public.
.......
After taking the manuscript paper from the waiter's hand, Xu Chuan returned to the wooden table again.
A white manuscript paper with a bit of off-white was spread flat on the table, and a black ballpoint pen began to outline mathematical symbols on it.
"...Starting from Weyl's Theorem 3.2, construct a bounded and connected open set Ω. Let Ω be a bounded connected area that satisfies the above conditions (≥2), and its boundary has the inner minkowski dimension δ∈(n
-1,n), then there is λ→ ∞, and there is:
n(λ)-?(λ)≤-,δ(λ/π2)δ/2....pn(t o(1)) o(δ?λ/π2)
"..."
"Suppose Ω(a) is a connected area, the side length of each square is li=a(i 1)-a(i), the function a(x) is strictly monotonically increasing, and limf(x→∞)
=limf(x→∞)(a(x 1)-a(x))=0..."
"It is further required that the area of Ω(a) is bounded, that is: |Ω(a)|2=∑∞/f(i=0)l2i
"Compute the inner minkowski dimension 6 of the boundary and the 6-dimensional minkowski capacity..."
"...."
Starting from the last inspiration, Xu Chuan defined the fractal dimension and the spectral invariant of the fractal measure of the Weyl-berry conjecture to a high-latitude boundary, and then used the Dirichlet function field to convert the Laplacian operator and the Laplace operator
Plath's hyperbolic equation, and then expand it....
Wonderful inspiration burst out in his mind again. The difference from last time was that this time, he had enough basic knowledge to build stairs to chase the inspiration.
Immersed in the process of solving problems and proving, he is like a criminal policeman collecting evidence bit by bit at a crime scene, and finally bringing them together to form a strong and reliable yoke to arrest the suspect hiding behind the scenes.
Same.
He is now collecting all kinds of available and reliable mathematical knowledge bit by bit, twisting it into a reliable hemp rope, and then connecting various mathematical theorems and calculation data these wooden boards together to form a reliable staircase leading to
The final Weyl-berry conjecture.
........
From the evening of the second day until the late night of the third day, nearly thirty hours, Xu Chuan did not close his eyes.
Except for going downstairs to eat, he never left this small hotel room.
So after missing the party on the second day and the exchange meeting and party on the third day, his senior brother Lin Feng called him on his mobile phone.
Hearing the vibration of his phone, Xu Chuan pressed it down without even looking at it.
But the other party seemed to be persistent and called one after another, which finally brought Xu Chuan back to his senses from his divergent thoughts.
"Hey, Senior Brother Lin, what do you want from me?"
With a tired voice, he passed it along the phone. On the other end of the phone, Lin Feng asked with concern: "Are you okay? Xu Chuan, do you have a cold or something? You didn't come to the exchange meeting and party today.
You missed such an important moment."
"I'm fine. I've had some inspiration in the past two days and have been thinking about things in my room."
Xu Chuan stared at the proof data on the manuscript paper and replied.
For him, if he missed the exchange meeting and party on the second and third days, he would have missed it.
Although the exchange meeting was important, it was nothing compared to what he had gained in the past two days.
This nearly 30 hours of busy work without sleep was not fruitless. He used the Dicrat function field to convert the Laplace operator and the Laplace hyperbolic equation, and then through differential equations he finally defined a fractal
framework, he successfully made the boundary?Ω measurable under this fractal framework.
At this point, there is only one final step left to prove the Weyl-berry conjecture, which is how to prove that the fractal dimension and fractal measure of Ω are spectral invariants.
As long as this problem is solved, the weyl-berry conjecture will become the xu-weyl-berry theorem.
In comparison, the missing lecture sessions at the exchange meeting and the conversations with others at the party seemed insignificant.
"Research problem? What problem to study? Forget it, as long as you are fine, remember to go to bed early. Don't forget that you have a report meeting tomorrow afternoon."
On the other end of the phone, Lin Feng's voice came through.
He hadn't seen Xu Chuan in the past two days, and he hadn't seen any familiar people around him, so he was a little worried about what happened to this junior brother here.
After all, it was my first time to come to the United States, and I was unfamiliar with the place. In addition, guns were not allowed in the United States, so it was still a bit unsafe.
As for now, since we are just studying the problem in the hotel room, it will be fine.
Although it's a pity that I missed the exchange meeting and the party, it's okay as long as everyone is fine.
