In 1859, Riemann published a paper entitled "On the Number of Prime Numbers Not Larger than a Given Value", which was only 8 pages long, and it was his only published treatise on number theory. ”

It was this mere 8 pages that laid the foundation for analytic number theory. ”

It can be seen that it does not necessarily require a large number of words to go down in history, and the quality of the article will always rank first. ”

"It is not clear on what grounds Riemann in 1859 made such a conjecture, perhaps on the instinct of genius.

"RH is equivalent to saying that all zeros of Ξ(ω) are real. ”

Riemann added, of course, needed to prove this, and he had done so, because a core expression had not been reduced to the point of being disclosed, so it had not been published. This is the biggest mystery in the history of number theory. ”

"You can see these words in any mathematics book or any paper, but what I describe next is an original ...... published for the first time."

Shen Qi wrote his "History of Number Theory" with passion, and when he got dry goods, his enthusiasm for writing was high.

Let the non-obvious set of zeros of the Riemann ζ function be:

{ρ1，1-ρ1，ρ2，1-ρ2，…… ，ρk，1-ρk，…… ρn，1-ρn}

The collective formula is schematically expressed as:

Any two non-obvious zeros with the feature of 'sum value 1, the same absolute value of the imaginary part' are matched as a pair.

For the sake of appellation, the author refers to this new treatment method as the 'twin matching method'.

In the following, the author will derive the core expression of ζ(s) through the 'twin matching method'. ”

Shen Qi worked hard to write a book, the core expression of ζ(s) is really going to be deduced by himself, and Riemann guesses that if it is really proved by himself, then this "History of Number Theory" will definitely be a big sell, and a book will become a god!

The "twin matching method" is the inspiration that Shen Qi has just realized, his originality.

The numbers game will come to an end one day, and Shen Qi decides to end the game of Riemann conjecture.

I couldn't sleep with excitement, and Shen Qi kept working until dawn.

"Therefore, under the treatment of 'twin matching method', the core expression of ζ(s) should be: ζ(s)=e^A+Bs∏∞n=1(1-s/ρn)(1-s/1-ρn)e^(s/ρn+s/1-ρn)...... So that's ......"

Shen Qi stood up, relieved his muscles, he looked at the rising sun outside the window calmly, and smiled.

The numbers game is not over, but Shen Qi has found the right way, which is a very important breakthrough.

"Therefore, the undisclosed expressions mentioned by Riemann are not one, but two, or even three, and the word 'one' is misdescribed, it should be 'group', which fully proves the Riemann conjecture and requires a core set of expressions. ”

Shen Qi fought all night and discovered a big secret, the whole world was tricked by Li Man, and he played it for more than a hundred years.

Whether Riemann was due to a clerical error, or a deliberate mistake, no one can say for sure.

This big secret, Shen Qi told his girlfriend on the phone for the first time: "I think I have found a solution to RH, I have created a new way to deal with it, let me tell you the general setting ......"

"There is no basis for what I say, I want to see the formula!" Ou Ye on the other end of the phone was excited.

Shen Qi: "If you follow my 'twin matching method', it proves that there should be a set of core expressions for RH, and I have deduced one of them. Next week I plan to visit Professor Gong at Columbia University, he is a top expert in this area, and I would like to hear his advice and advice. I'll show you the formula next week, I need to perfect it. ”

Ou Ye: "Say you will come to see me in a month, it's really only a month." Well, see you next week. ”

After hanging up the phone, Shen Qi slept for a while, and after getting up, he continued to deduce other expressions that existed theoretically.

The problem, however, is that based on the "twin matching method" and the first expression, you can't get the second expression anyway.

"Hey, I've tasted a little bit of sweetness, but I want to get it all, if only I could get to level 13. Shen Qi looked at the system, and it took 4 million points to upgrade from level 12 to level 13, which means that more than 10 papers from the four major journals will be sent.

From September of the previous year to now, a year and a half have passed, and Shen Qi has published three papers in the four major journals and ten new papers in the four major journals, which will take several years.

"I need to listen to the crowd and make the most of Princeton's superior resources to win this important battle as a team. ”

Shen Qi walked towards Professor Mueller's office, knowing that Professor Mueller's mind was clear.

A year ago, Müller arranged for Shen Qi and Mary to work on a joint project to derive two recursive expressions for ζ(s).

For various reasons, this subject is messed up.

But Professor Müller's intuition was accurate, he was German, and he must have studied Riemann's manuscript in German.

Professor Müller had long had a hunch that there was more than one "undisclosed expression" that Riemann was referring to.

"Jiang is still old and spicy, and it is becoming more and more difficult for the elder Muller to complete the calculation and derivation of high-intensity, big data, but his strategic vision and mathematical intuition are extremely sharp. "Shen Qi now understands Professor Mueller more and more, Lu Yao knows horsepower, and after being in contact with a person for a long time, he can discover his real strengths and weaknesses.

Mueller's office.

Shen Qi wrote on the blackboard the setting principle of the "twin matching method" and the first expression.

"Oh my God!" Muller was shocked, staring at the blackboard for a long time, speechless.

Shen Qi knocked on the blackboard: "Professor Mueller, what do you think of my new setting?"

Old man Muller talked about juvenile madness, and he was particularly excited: "With this new 'twin matching method' and the first expression, Shen Qi is qualified to give a report at the International Congress of Mathematicians, and the IMU should give you at least 30 minutes of reporting time! This is a major breakthrough in the Riemann conjecture! If you can deduce all the expressions that exist theoretically, God, the Riemann conjecture will be solved!"

Shen Qi said calmly: "Professor Mueller, I need your help, I need the help of the whole team. Thinking back to your and Mary's views a year ago, I realize that I was very stupid and stubborn. Now, let's get the Muller battleship back on sail, and I hope that through the strength of the team and the proper scheduling of resources within the department, the proof of RH will finally be completed. ”

Müller was both surprised and relieved: "Are you sure you are doing this, strange? Now you are fully capable of doing the proof of RH by yourself, and in a few months I will no longer be your mentor, and then you can start the project on your own." ”

Shen Qi smiled: "Allen, even if you are not my mentor, we can still become partners." Thank you for taking care of me for more than a year and giving me a free academic environment, which has played a key role in my growth. Remember the 'Mill-Shen theorem', we will always be partners, and this theorem will always exist. ”