The thoughts in his mind were circulating, Xu Chuan was stunned, and a faint path appeared in his dilated pupils.

The Riemann conjecture is a question that has been raised in order to study the π(x) function, which is a conjecture about the zero-point distribution of the Riemannian ζ function ζ(s).

When Riemann was appointed Corresponding Member of the Berlin Academy of Sciences in 1859, Riemann presented his only paper on number theory, and the only one that did not contain geometric concepts at all: "On the Number of Prime Numbers Less than a Given Value".

This paper is not long, only nine pages, but it can be said that it ushered in a new era in the history of mathematics in analytic number theory.

In the paper, Riemann gives an accurate expression of the prime counting function: π(x)=∞∑n=1·μ(n)/n· J（nx）。

Undoubtedly, this is the core of the results of the distribution of prime functions.

If the Riemann conjecture made him world-famous, it was a real pioneering work to elevate the study of π (x) from a real straight line to a complex plane by introducing the Riemann Zeta function.

Using the method of complex analysis, he combined algebra and geometry, and pioneered the development of modern mathematical branches such as topology and differential geometry, bringing the development process of algebra into the field of the fourth dimension.

By using the concept of curvature to define space, Riemann opened up a new field of non-Euclidean geometry and was undoubtedly a true mathematician.

Of course, what made him famous all over the world was the Riemann conjecture.

This conjecture of the century, defined by the Clay Institute of Mathematics as the Seven Millennium Puzzles, involves thousands of mathematical formulas based on it.

If the Riemann conjecture comes true, then at least more than 2,000 mathematical formulas will be elevated to theorems; If the Riemann hypothesis is proved to be negative, it will turn the entire mathematical community upside down!

For Xu Chuan, today he is not thinking about this, but about some things he studied when he went to St. Petersburg to attend the State Congress of Mathematicians last year.

The correlation function 'stochastic Ermi matrix eigenvalue' triggered by the Riemann conjecture!

If, by means of the multi-complex variable function theory, the polynomial function on the yoke matrix is referenced, then the Jensen polynomial and the Taylor/McLaughlin series are introduced

Perhaps, he knows what to do!

The thoughts and fragments in my mind are constantly splicing, and a path that seems to be in my eyes emerges.

The black pupils that emanated gradually condensed back, Xu Chuan's eyes flashed with joy, and after his thoughts returned, he excitedly grabbed the arm of the figure in front of him, and gave a warm hug, and said incoherently excitedly.

"Hahahaha, I found it, I got it! I know what to do! ”

Excited voices and wanton smiles resounded throughout the office.

On the one hand, Liu Jiaxin, who was hugged by Xu Chuan, stiffened her whole body, feeling the heat and strength from her body, and a touch of red quickly floated on her face, red to the root of her ears.

In the excitement, Xu Chuan didn't care about this, he quickly let go of the other party, and quickly said: "Jiaxin, help me find a room, and then lend me some manuscript paper!" ”

The inspiration in his mind had reached its peak at this moment, and he couldn't care where it was.

Not only the Riemann conjecture, but also the correlation function between the Riemann conjecture and the eigenvalues of the stochastic Ermi matrix cannot be ignored.

It corresponds to a function in physics that describes the distribution of energy levels in multi-particle systems under interaction, and if his previous research had not been problematic, perhaps in the field of number theory, he would have come into contact with the obsessive 'Einstein Rosen Bridge'!

Late at night, in the building of Chuanhai Network Technology Co., Ltd., in the cubicle next to Liu Jiaxin's office, under the bright light, Xu Chuan's pupils were bloodshot, but his face was full of excitement.

The tip of the pen was lightly touched on the paper, and the ballpoint pen in his hand was pinched, and he quickly wrote out the mathematical formulas and basic theories of calculation on the white A4 paper.

The thick stack of manuscript paper in front of him was already covered with mathematical formulas, and the floor was littered with crumpled scrap paper.

【π(x)=∫2x·dt/ln t+ O（x^1+2+ε）.】

This is the asymptotic formula of the π(x) function, through which the Riemann conjecture can be further derived: [ζ(s)=∏p(1-p^(-s))^-1]

However, what Xu Chuan needs to do now is not to expand the Riemann conjecture through the asymptotic formula, but to further expand and compress it through the function theory of multiple complex variables.

The Riemann conjecture was not so easy to solve, and he needed a tool to shrink Re(s) to 1/2 before he could make his way to the biggest mountain in mathematics.

1/2, or 0.5, is a very special figure in the Riemann conjecture.

Since the Riemann hypothesis was proposed in the 19th century, countless mathematicians have been fascinated by it.

For a long period of time, mathematicians have called a straight line with Re(s)=1/2 on the complex plane a critical line.

Therefore, the Riemann conjecture can also be expressed as follows: all non-trivial zeros of the Riemann ζ function are located at the Re(s) critical point, and the real roots of the non-trivial zeros are 1/2.

Mathematical rigor and logic aside, in the simplest terms, you can think of: "According to an important mathematical formula, we can draw many infinite points." ”

"And some of these points are arranged in a horizontal line, and the other part is arranged in a vertical line, but all the points are on these two lines, and none of them slip through the net."

The Riemann conjecture is one such mathematical formula, in which a line is a straight line based on 1/2.

However, since there are infinitely many of these points, there is theoretically no way to prove that all the points are on these two lines, because it can never be verified.

Conversely, as long as a point is found that is not on the line, the Riemann conjecture is overturned.

But up to now, the mathematical community has used computers to verify that the first 1.5 billion such points are all in accordance with the arrangement of the Riemann hypothesis.

No one can find a point that is not on the line.

Therefore, the Riemann conjecture is usually regarded as a theorem in the mathematical community, and many mathematical formulas are based on the foundation on which it is established.

The long time passed little by little unconsciously, and the lights in the cubicle were bright, and Xu Chuan didn't know what time it was.

[When Re(s)≤0, ζ(s)=2π^8-1·sinπ8/2Г(1-s)ζ(1-s)】

After quickly writing down a mathematical formula on the manuscript paper with the ballpoint pen in his hand, he fell into deep thought.

After half a ring, he scratched his head and put down the pen in his hand with some pauses of 'trouble' and 'happiness'.

After being reminded by his senior sister Liu Jiaxin, he found out where the problem he had studied before, and vaguely found a little direction for his previous research on Einstein Rosen Bridge.

But by mistake, he did not find any ideas for the direction he was going to study, but had a little inspiration for the Riemann conjecture.

Looking at the manuscript paper spread out on the desk, Xu Chuan pursed his lips, which is the derivation of the ζ(s) function and the ζ(1-s) function through the Poisson summation formula, which is one of the core steps of the verification of the non-trivial zero when Re(s)≤0.

In layman's terms, it is to weaken the Riemann conjecture, and then solve the weakened Riemann conjecture, that is, the weak Riemann conjecture.

In fact, this is what the modern mathematical community has been doing.

Studying the number of lower bounds of the zero scale on the critical line is the best method recognized by the mathematical community since the emergence of the critical zone idea of the Riemann conjecture.

In the ζ function of the Riemann conjecture, all non-trivial zeros are located at the Re(s) critical point, and the real roots of the nontrivial zeros are 1/2.

This is conjecture, and it has not been proven.

But at present, the mathematical community has managed to reduce the non-trivial zero points of the ζ function of the Riemann conjecture to the critical zone of 0-1, which is close to 0.5.

To put it simply, I can't prove that the real roots are 1/2, so I'll prove that they are all between 0 and 1.

It's not standard, but it's at least easier to understand.

The critical zone of thought, the lower bound, is one such idea.

By continuously advancing the distance of 0-0.5, the non-trivial zero points are gradually approached to 1/2.

And on this path, a large number of achievements have emerged in the mathematical community.

For example, in 1975, Levinson of the Massachusetts Institute of Technology proved that No(T) was > 0.3474N(T) before he died of cancer. In 1980, Chinese mathematicians Lou Shituo and Yao Qi improved Levinson's work a little, and they proved that No(T)>0.35N(T).

The best results of the current research on the Riemann hypothesis have been proved by the method of constantly approaching the critical zone.

Unfortunately, a century and a half after the Riemann hypothesis was proposed, the progress of research on the Riemann hypothesis, including the promotion of the critical zone, is still far away.

Xu Chuan didn't know if this path was the right one, but for now, he seemed to have found another way to get close to the non-trivial zero.

Although this is only a little bit of thinking, and it needs to be continuously improved in the future, it can be said that if this idea is released by him, it will definitely shock the entire mathematical community and set off a wave of Riemann conjecture.

It's just that it's not what he wants.

The 'stochastic Ermi matrix eigenvalues' pair correlation function that he wanted to study has not made much progress today.

Even in the dark, he had an intuition that perhaps only by completely solving the puzzle of the Riemann conjecture could he possibly come into contact with the secret that belonged to 'time and space'?

Prime numbers, perhaps really connected to time and space, hide the deepest mysteries of the universe.

PS: I just started work in the new year, and I was a little busy, and I worked overtime unexpectedly, plus I recently read the Riemann conjecture and the paper materials of the space-time wormhole, and I thought about it.