Chapter 257: Finally Obtained Patent

"...Based on the paper published by Professor Zellberg in 1995, I further improved the theory of the large sieve method through the principle of topology. Then, when proving the Polignac conjecture, in order to solve the problem of dividing the distance between prime numbers from 2 to the difficulty of extending to infinity, and I introduced the method of group theory into it.”

"The key step can be reflected in the first three lines on the second page of the paper. As for some preparatory work on group theory, I will explain it later."

A pair of eyes converge on one point.

Feeling the truth-seeking sight, Lu Zhou turned his PPT to the audience, and continued to preach calmly.

"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), the absolute convergence of the series δd(n)=∑Td(n,q) can be obtained."

"This step is very critical. It comes from the proof of the weak Goldbach's conjecture published by Mr. Helfgott in 2013."

"However, our goal is different from the circle method. We are not to perform Fourier analysis in number theory on the function on the circle to find uncertain upper and lower bounds, but to approximate the distribution of prime numbers."

"Starting from this step is the key to the 'group construction method'..."

In fact, Lu Zhou was not the first person to try to integrate the circle method and the large sieve method, just like he was not the first person to introduce group theory and topology concepts into number theory problems.

A similar attempt was made by Helfgott, and it was reflected in the paper he published in 2013.

Although he mainly used the circle method, some of the conclusions were also drawn through the big sieve method.

According to his own description of the sieve method and the round method in an interview, he called the two methods like the positive and negative sides of a coin. How to use it depends on how you toss the coin.

Regarding the core theory of the group construction method, Lu Zhou explained it in detail, because this is the essence of the whole paper.

Huaguo Analytical Number Theory School, which once made outstanding contributions to the world's number theory research, has been in decline since the death of Mr. Hua Luogeng. Now it is like a "cultural relic", preserved in Shuimu University, and even some good people use " Annihilation" has been used to describe it.

The reason is that some of the blame has to be borne by veteran academics. After all, it is too much to monopolize the voting rights of academicians. Although one can be a scholar without money and status, no future in this environment means no fresh blood.

Of course, the fault is not entirely on others, but part of the reason comes from oneself, that is, later generations cannot make innovations in the theory of predecessors. After Mr. Hua passed away, his knowledge stagnated along with his life. not before.

If the Huaguo School of Analytical Number Theory is to regain its brilliance in the international arena, it must inject new things into it.

Lu Zhou hopes that the professors who have listened to his lectures can bring his methods or theories back to the classrooms of Shuimu, Yanda, Aurora, Kaida and other universities, and even project topics.

To revive a school, or to establish a school, it is not enough to rely on the strength of one person.

If someone solves a deep mathematical proposition through his theory, he will be very honored.

And Lu Zhou also believes that the theory of group construction method does not stop at Goldbach's conjecture, and many problems of stacking prime numbers can be analyzed through this line of thinking.

"...In the end, we introduce the Bombieri theorem, and we can get the formula (29) in the PPT. And through this critical step, we can find the last line of expression."

[Px(1,1)≥P(x,x^{1/16})-(1/2)∑Px(x,p,x)-Q/2-x^(log4)...(30) 】

At this point, the format of the formula is actually the same as Mr. Chen's paper.

The group construction method is derived from the large sieve method.

And in the end, everything must return to the final proposition.

"...From formula (30), Lemma 8, Lemma 9, and Lemma 10, Theorem 1 can be finally proved, that is, the Goldbach-Lu theorem is established."

The moment the voice fell, warm applause resounded in the auditorium of a thousand people.

Facing the scholars and professors in the audience, Lu Zhou bowed slightly, and walked off the podium calmly amidst applause.

Back behind the scenes.

In the lounge, Lu Zhou saw Professor Feng Keqin from Shuimu University, Mr. Hua Luogeng's closed disciple.

The old man's eye sockets were a little red, he took a deep breath, and said in a calm and trembling tone.

"Your presentation was as stunning as your thesis...Thank you!"

Lu Zhou smiled and said humbly, "You're so honored. I once read your Introduction to Algebraic Number Theory in the library of Jinling University. It inspired me a lot."

"Those things were written in the past, and now they can't keep up with the times," Mr. Feng coughed lightly in embarrassment, looked at Lu Zhou, paused for a moment, and said in a sincere tone, "Actually, I am writing a This textbook is also about number theory. Your speech just now inspired me a lot, and I would like to include some excerpts of your speech today into the textbook... May I ask?"

Writing a book is a very tiring task. It needs to consult a large amount of literature and research everywhere, which takes up a lot of time that should be used for research.

Unless it is difficult for a person to achieve academically in his later years, Lu Zhou himself would never consider doing these things.

However, someone has to do it.

Lu Zhou readily agreed.

"sure."

...

The next day, in the same auditorium, Lu Zhou accepted the doctorate and title of honorary professor from Jinling University.

As a result, the affairs of Jinling University have finally come to an end.

But before embarking on the journey home, Lu Zhou still has one important thing to do.

Before leaving Princeton for Stockholm, he received a call from the patent attorney named Han Tianyu, telling him that the patent authorization documents from various countries had been obtained, and asked him when he would have time to come and get them.

After calling and making an appointment, Lu Zhou found the patent attorney named Han Tianyu and got the authorization document of the international patent from him.

So far, he has basically obtained the patent authorization documents from mainstream countries.

These patents have basically covered 80% of the global market, as long as someone uses his technology in a product, he can benefit from it.

As for the patent authorization of some developing countries with smaller markets, Lu Zhou is not interested in doing it.

Not to mention the various patent exemption privileges of some developing countries in the WTO, such as some small countries in Central Africa, maybe Nokia has not been fully popularized, and when the industry develops the market there, I am afraid that the patent validity period of 20 years will not be enough. It may not be possible to do it.

And by that time, maybe other new technologies will be developed in his laboratory.

"The next thing is to write a paper and promote this technology." Looking at the patent document in his hand, Lu Zhou couldn't help feeling softly in his heart, "Chemistry... the meal ticket for the next few years depends entirely on you."

He has made up his mind.

After the vacation is over, I will start writing as soon as I return to Princeton.

Not only because of money, but also a generous mission reward is waiting for him.

As for the publication of "Science" after the thesis is completed? Or publish "Nature"?

This is a question worth thinking about.