"You can ask questions about number theory and functional analysis now. Mathematics problems in other fields, after the guidance course is over, I welcome you to come to me to discuss them at any time."

Shen Qi emphasized the rules. The 2-hour guided course time should focus on number theory and functional analysis. Otherwise, if you ask about geometry, he will ask about topology, and the classroom order will be in chaos.

"Okay, then I have no problem." Ajie shook his head. He was not very interested in number theory and functional analysis, but these two courses are compulsory courses for students in mathematics. In short, it would be great if he got the credits.

"Yes, I have a problem, number theory." At this time, an Arab-faced student spoke. His name was Muhammad. According to him, his family was very wealthy when he was a child. He received a good education. Later, he became poor in war, so he lost school for more than a year.

"Please express your doubts, Mohammed." Shen Qi stood in front of the blackboard and made a gesture of invitation.

Mohammed is several months older than Shen Qi. He just joined Shen Qi's tutoring class this semester, and he is not as admiring as Ajie and four others.

"I have looked at Riemann's manuscript, and he wrote in the manuscript that these properties of ζ(s) are derived from one of its expressions, but I have not been able to simplify this expression to a form that can be published in the public."

"That's right, this is Riemann's original text." Shen Qi nodded. He had studied Riemann's manuscript less than a hundred times and was familiar with it.

"So strange, can you tell me what form should it be in Riemann's not published expression in the manuscript?" asked Muhammad.

"Mumhamed, this question is so wonderful!" Shen Qi's eyes shone, and then smiled helplessly: "If I could write this legendary expression, I could make at least 45 minutes of report at this year's International Mathematician Conference. But unfortunately, until today, I have not received an invitation from IU."

"It seems that the proof of Riemann's conjecture will last for 100 years." Mohammed said, spreading his hands, and he did not receive a satisfactory reply and was slightly disappointed.

Shen Qi really couldn't answer the expression in Riemann's manuscript. If he tinkered with this expression, it would be not far from proving the Riemann conjecture.

Whether the expression Riemann mentioned, which is "not simplified to be published to the public" has really existed and in what form it has existed is a mystery in the history of mathematics.

Research on Riemann's manuscripts has lasted for more than a hundred years. Mathematicians believe that even if this expression is not simplified to the most perfect form, it is still of great significance to cracking rh, after all, it represents Riemann's core idea.

The god-level masters in the history of mathematics all have a small problem, which is that they like to play pranks. They perfectly lay the foreplay that makes people's desire burn, and then there is nothing else.

The Ferma Terrier is "too little blank space in the book", and the Riemann Terrier is "not simplified to a form that can be published in the public."

Shen Qi has included these two memes in his "History of Numbers". Focusing on the Fermat Terrier, he will write a whole volume of "Fermatites and Fermat Series of Conjectures".

The material has been found, and most of the important, the famous Fermat series guesses have been proven. The rest is to spend time sorting out and write the history of number theory in that period where Fermat is in as interesting as possible without losing its professionalism.

Shen Qi also collected a lot of materials around the Riemann genre, but the most critical issue is that the Riemann conjecture has not been fully proved. The volume of "Riemann and Riemann conjecture" cannot be perfectly concluded, and may be forced to be completed in an unfinished manner.

Writing history of numbers and not writing Riemann's conjecture and Goldbach's conjecture is an irresponsible act.

However, all the books about Li Chai and Gechai in the world are to introduce these two conjectures to let readers know the nature of Li Chai and Gechai, and there is no practical information.

Shen Qi wanted to write something real, but because of his limited level, his "History of Numbers" may have become a formality and turned into a hydrology book.

After finishing the guidance course, Shen Qi came to the Flint Library and checked the Riemann manuscript again.

The bookshelf length of the main library of the Flint Library is 70 miles long, all of which are open.

Readers can enter the library to check the books and magazines they need, from first-year freshmen to Nobel Prizes and Philippine Prizes professors, from auxiliary personnel to principals, treating them equally.

Copies of ordinary books and published papers can be borrowed from the publication, rare books, ancient books, and manuscripts cannot be borrowed from the publication, but can be read in the reading room.

The original Riemann manuscript is in German and is collected in Germany.

The Puda Flint Library contains an English version of the manuscript, which was translated by Von Neumann when he was teaching at Puda.

Von Neumann is a versatile talent, knowing everything about mathematics, computers, nuclear weapons, and biological weapons, and has achieved top-notch skills.

The English version of Riemann manuscript translated by von Neumann is only 8 pages. Shen Qi can recite it backwards. He studied it again today, carefully reading one word at a time and space, trying to figure out Riemann's thoughts more than a hundred years ago, hoping to find even a little clue.

Riemann's conjecture only has one sentence: "All the re-zero points of ζ(s), that is, all the zero points of ξ(s) are on the straight line σ=1/2."

Riemann himself did not prove this conjecture. If he wanted to prove it successfully, it should now be called Riemann theorem.

For the Riemann conjecture, Riemann gave an important prediction of the property of ζ(s), namely the equation that everyone knows now:

π^-s/2γ(s)ζ(s)=π^-(1-s)/2γ(1-s)ζ(1-s)

However, Riemann himself said: "These properties of ζ(s) are derived from one of its expressions, but I have not been able to simplify this expression to a form that can be published in the public."

So this expression that needs to be simplified is the key among the keys, and it is the key to cracking the Riemann conjecture.

"Actually, my previous idea was not wrong. I tried to find the two recursive expressions of ζ(s), which coincided with Riemann's derivation logic. Riemann, what is the form of this undisclosed expression you mentioned?"

Shen Qi stayed in the library for one night, and seemed to have gotten a little bit of inspiration.

But this inspiration is very ethereal, and Shen Qi cannot write it out in a concrete way. The deduction, imagination and judgment of the level 11 mathematical level are still a little lower. It would be great if he could reach level 12.

Back at the accommodation apartment, Shen Qi brushed the submission system of "Mathematical Inventions".

“Collection!”

Shen Qi was surprised. He really had his wishes come true recently, and he would do whatever he wanted.

The paper "Shen's Theorem for the Near Forces" has been officially included in "Mathematical Invention", one of the four major journals.

It will definitely be included. Professor Weiteng and Director Feverman have confirmed that there is no problem with the "Shen's near-force theorem".

The two Philippine Award winners said there was no problem, and that was definitely no problem.

System: "New achievements! Congratulations to the host for publishing a paper in "Mathematical Invention", one of the four major mathematical journals, with a basic reward of 50,000 points of academic master points, multiplied by the if value of the journal 3.331, and multiplied by the mathematical master talent coefficient 2.0. The final reward amount is 333,100 points of academic master points. The balance of 2021,400 points of academic master points, please confirm it."

"These 300,000 points of academic master's points are just right." Shen Qi expressed satisfaction.

Currently, "Mathematical Invention" contains papers on "Shen's Near Force Theorem", but Imu has not yet officially recognized it.

After a while, Imu admitted the "Shen's near-force theorem" and there should be subsequent points income for top students.

"Mathematics is promoted to a senior master." Shen Qi took out 1999862 points of academic master's points and upgraded mathematics to level 12.

To level 11 to level 12, you need 2 million points for top students. Shen Qi has obtained 138 mathematical experience points through daily experience values ​​in recent times, so it is enough to spend 1999862 points for top students.

System: "Congratulations to the host's mathematical level for upgrading to level 12, and the host's logical deduction, observation, judgment, imagination, memory and other indicators in the field of mathematics have significantly improved compared with the previous level."

Host, Shen Qi

Age, 22 years old

Mathematics Level 12, 0/4 million

Physics Level 6, 11.23/150,000

Sports Level 5, 3019/50,000

English Level 5, 9.87/50,000

Chinese Level 5, 999/50,000

Political Level 5, 13.6 million/50,000

Chemistry Grade 3, 502/5000

Biological Level 3, 520/5000

History Level 2, 1139/3000

Geography Level 2, 689/3000

The points of the top scholars: 21538 points

Level 11 is the master level, level 12 is the senior level, level 13 is the top level, level 14 is almost invincible, and level 15 is so lonely.

Shen Qi, who was successfully promoted to a senior master of mathematics, suddenly got the illusory inspiration, which seemed to be concrete: "I thought of it! I thought of it! Riemann in 1859, he probably wanted to deduce it like this..."
Chapter completed!