“…… Based on the paper published by Professor Zelberg in '95, I further refined the theory of the large sieve method by using the principles of topology. Later, when I proved the Polygnac conjecture, in order to solve the difficulty of generalizing the prime number spacing from 2 to infinity, I introduced the method of group theory. ”

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

A pair of eyes converge a little.

Feeling the truth-seeking gaze, Lu Zhou faced the audience, turned the PPT over a page, and continued to preach calmly.

"We remember 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), we can get the series δd(n)=∑Td(n,q) absolute convergence. ”

"This step is crucial and comes from the proof of the weak Goldbach conjecture published by Mr. Hutfgot in '13."

"However, our goal is different from the circle method, we are not to perform a Fourier analysis of the functions on the circumference of the circle, to find uncertain upper and lower bounds, but to approximate the distribution of prime numbers."

"From this step onwards, it is the key ...... of the 'group construction method'"

In fact, Lu Zhou was not the first to try to fuse the circle method with the large sieve method, just as he was not the first to introduce the concepts of group theory and topology into number theory problems.

Hellgot made a similar attempt, and it was reflected in his paper published in '13.

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

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

For the core theory of the group structure method, Lu Zhou spoke in great detail, because this is the essence of the whole paper.

The Huaguo School of Analytic Number Theory, which has made outstanding contributions to the study of number theory in the world, has gone into decline since the death of Mr. Hua Luogeng, and now it is like a "cultural relic", which is preserved in Shuimu University, and some people have even used the word "annihilation" to describe it.

The reason for this is that part of the pot has to be carried by the old academic valves, after all, the monopoly of the voting rights of academicians is indeed excessive, although there is no money and no status to do learning, but in this environment, no future is equivalent to no fresh blood.

Of course, the pot is not all in others, and part of the reason comes from itself, that is, the descendants cannot make innovations in the theories of their predecessors.

If we want the Chinese school of analytic number theory to shine again internationally, we must inject something new into it.

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

It is not enough to revive a school, or to build a school, by the power of one person.

If someone solves an esoteric mathematical proposition through his theory, he will be honored for it.

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 idea.

“…… Finally, we introduce the Bombieri theorem, and we can get the equation (29) in the PPT. And through this crucial step, 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 equation is actually no different from Mr. Chen's paper.

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

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

“…… From Eq. (30), Lemma 8, Lemma 9, and Lemma 10, it can be finally proved that Theorem 1, that is, the Goldbach-Lu theorem, is true. ”

When the words fell, the auditorium of 1,000 people resounded with warm applause.

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

Back behind the scenes.

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

The old gentleman's eyes were a little red, he took a deep breath, and spoke in a steady tone with a hint of trembling.

"Your speech is as impressive as your thesis...... Thank you! ”

Lu Zhou smiled and said modestly: "You have won the award, I once saw your introduction to algebraic number theory in the library of Jinling University, and it inspired me a lot. ”

"Those things were written before, and now they are almost out of step with the times," Mr. Feng coughed lightly embarrassedly, looked at Lu Zhou, paused for a moment, and said in a sincere tone, "Actually, I am writing a textbook, which is also about number theory." I have been very inspired by your speech just now, and I would like to include an excerpt from your speech today in the textbook...... Is that possible? ”

Writing a book is a very tiring task, requiring a lot of literature to be consulted and researched, which takes up a lot of time that should be spent on research.

Unless it is difficult to make academic achievements in his old age, Lu Zhou himself will never consider doing these things.

But someone has to do it.

Lu Zhou readily agreed.

"Absolutely."

……

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

As a result, the matter on the side of Jinling University has finally come to an end.

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

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

After making an appointment on the phone, Lu Zhou found the patent agent named Han Tianyu and got the authorization documents of the international patent from him.

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

These patents have basically covered 80% of the global market, and anyone who uses his technology in their products can benefit from it.

As for some of the smaller market sizes in development. The country's patent is authorized, and Lu Zhou is not interested in doing it.

Not to mention some in development. The various patent exemption privileges of the state, such as some small countries in Central Africa, may not be fully popularized by Nokia, and when the industry develops the market there, it may not be possible to achieve it even if the patent validity period of 20 years has expired.

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

"The next step is to write a paper and promote the technology." Looking at the patent documents in his hand, Lu Zhou couldn't help but sigh softly in his heart, "Chemistry...... It's up to you to get a meal ticket for the next few years. ”

He's made up his mind.

When the vacation is over, I start writing as soon as I get back to Princeton.

Not only because of the money, but also a generous task reward was waiting for him.

As for the completion of the paper, what about the publication of Science? Or do you want to post "Nature"?

It's a question worth pondering.