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**Translator:**Henyee Translations**Editor:**Henyee Translations

Based on the paper published by Professor Zellberg in 1995, I further improved the large sieve theory using topology. Then, in order to expand the Polignacs conjecture, I introduced a group theory method.

The main step is in the first three lines of the second thesis page. As for some of the group theory foundations, I will explain that later.

Pairs of eyes stared at Lu Zhou.

Lu Zhou sensed that people were looking at him. He turned the Powerpoint Page and continued to speak.

We record S1(q,)=e(m3/q), C1(q,)=e(m3/q2), brought into Td(n,q)=S1(q,d3) |C1(q,d3)|e(-an/q)/q2(q), the order d(n)=Td(n,q) can be obtained.

This step is crucial. It comes from the 2013 weak Goldbachs conjecture proof from Helfgott.

However our goal is different than the circle method. We are not trying to perform Fourier analysis in the number theory function. Instead, we are trying to approximate the distribution of prime numbers.

Next up is the Group Structure Method

Actually, 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 use topology in a number theory problem.

Helfgott had tried similar methods, which were seen in his 2013 thesis.

Although he mainly used the circle method, there were some conclusions that used large sieve method.

In an interview, Helfgott said that the two methods were like two sides of a coin. How one used the methods depended on how one threw the coin.

Since it was the essence of the whole thesis, Lu Zhou carefully explained the core theory of Group Structure Method.

The analytic number theory field in China had made outstanding contributions to the world of number theory. However, since the death of Mr. Hua Luogeng, the entire industry died down. It was like an army without a general.

Although they said academia could be done with no money and status, there was just no fresh blood coming into the field.

Of course, there were other reasons as well. After Old Huas death, the later generations could not innovate based on Old Huas theories, and the knowledge output thus stagnated.

If someone wanted to make Chinas analytical number theory field return to its glory, they would have to add something new.

Lu Zhou hoped that the professors who listened to his report would bring his theory back to the classrooms of Shuimu University, Yan University, and Aurora University.

Reviving an academic field, or building one, could not be done with just one person.

If someone solved a mathematics problem through his theory, he would feel honored.

Lu Zhou believed that the Group Structure Method had more applications than Goldbachs conjecture. Many problems revolving around the prime numbers could be solved with this method.

Then we use Bombiere theorem, on page 29 of the powerpoint. Then through this crucial step, we get the last expression.]

[Px(1,1)P(x,x^{1/16})-(1/2)Px(x,p,x)-Q/2-x^(log4)(30)]

From here, the formula was no different than Mr. Chens thesis.

The Group Structure Method was derived from the large sieve method.

At last, it came full circle.

From the equation (30), Lemma 8, Lemma 9, Lemma 10, we can finally prove the theorem 1, that is, the Goldbachs theorem.

The moment Lu Zhou finished speaking, applause filled the auditorium.

Lu Zhou bowed toward the professor and scholars. He then turned around and quietly walked off stage.

Backstage

In the lounge, Lu Zhou saw Professor Feng Keqin from Shuimu university. He was one of Hua Luogengs closest disciple.

The old mans eyes were a little red. He took a deep breath and spoke in a steady tone, Your speech and thesis were shocking Thank you!

Lu Zhou smiled and said humbly, Youre too kind. I have read your introduction to algebraic number theory textbook at the library of the University of Jin Ling. It greatly inspired me.

I wrote that book a long time ago, but I cant keep up with the times anymore, said Professor Feng with a smile. He then looked at Lu Zhou as he said sincerely, Actually, Im writing a textbook on number theory. Your speech has inspired me, and I want to write the contents of your speech into the textbook Is that okay?

Writing a textbook was a very time-consuming thing. It required a large consumption of documents and research.

Most people would not write textbooks until they were very old, and could not do research anymore. Lu Zhou would never want to write a textbook.

However, someone had to write the textbooks.

Lu Zhou agreed immediately.

Of course you can.

The next day in the same auditorium, Lu Zhou received a PhD from the University of Jin Ling and the title of honorary professor.

As a result, his journey at the University of Jin Ling had finally come to an end.

However, before Lu Zhou departed on his new journey, he had one more important thing to do.

Before he went to Stockholm, he received a call from his patent agent. The patent agent, Han Tianyu, told him that the patent documents had been processed, and asked Lu Zhou when he could collect them.

Lu Zhou made an appointment and found the patent agent called Han Tianyu. From Han Tianyu, Lu Zhou obtained the international patent authorization documents.

Therefore, he had obtained patents from most major countries.

His patents basically covered 80% of the global market. If someone used his technology, he would benefit from the product.

As for some of the smaller countries, Lu Zhou was not interested in applying for a patent there.

Since most of them were developing third world countries, Lu Zhou could always apply later.

Maybe by then, he would have come up with another better and more improved technology.

The next step is to write a thesis and promote this technology, said Lu Zhou as he looked at the patent documents. He then said, Chemistry Ill have to depend on you to make money.

He made up his mind.

Once he was done with his vacation, he would start writing the thesis back at Princeton.

It was not only for money. It was because a fat mission reward was waiting for him.

*After I finish writing the thesis, should I post it in Science or Nature?*

*This is a question worth considering.*

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