Taking the high-speed train back to Jinling from the capital, Xu Chuan first went to the Xinghai Research Institute, and after presiding over the daily work there, he went back to his villa.

After saying hello to Zheng Hai, he shrank in his study and studied it intently.

The study of the weak Riemann conjecture already had a preliminary idea, and there was no reason why he should not continue to study it.

Prime numbers are not only linked to the purest mathematics, but there may also be many mysteries worth exploring.

For Xu Chuan, it was a long time ago to devote himself to the study of a mathematical conjecture for a long time.

If we really want to go back, we may have to go back to the completion of the 'unified framework theory of strongly correlated electronic systems'.

In the follow-up, whether it was the research on the existential and mass gap problem of Jan Mills or the Einstein Rosen Bridge, it actually did not take him much time or devote himself to it.

The former is the result of the research of the previous life, and even if it is the second way of verification of the quality gap, it is just a sudden inspiration on the lecture table, and it is only the follow-up as a whole.

As for Einstein Rosen Bridge, not to mention it, so far he has only scratched the surface of the problem.

Today, the study of the Riemann conjecture has made him devote all his energy to it.

However, this feeling is not unfamiliar to him, and even, when he fully enters this field, the feeling of mathematics is like information engraved in DNA, familiar and long-lasting.

Especially when all his attention was focused on the black mathematical symbols on the white manuscript paper, it was as if the whole world had disappeared, leaving only the Arabic numerals and ancient Greek symbols in front of him.

The pen glides smoothly across the paper, leaving behind wonderful characters, as if every stroke is a poem, and every word is a bright star that lights up the whole world.

In the middle of the night, a gentle lamp is lit in the quiet study, and the Purple Mountain outside the window seems to be sleeping, and occasionally there are some rustling sounds, just like love words in a dream.

Staring at the manuscript paper on the desk, Xu Chuan had a bright light in his eyes, and his mouth was softly muttering.

"The zero point of Reimannζ is inextricably related to prime numbers, the most direct of which is the prime count function π (x) can be represented by the zero point of the ζ. The prime counting function is to give the number of prime numbers less than or equal to x. ”

In order to deduce the law of π(x), both Gauss and Legendre did a lot of numerical calculations., and they respectively guessed that when x →∞, π(x) x/ ln x, where "" denotes that the ratio of the two functions tends to 1, and ln x is the natural logarithm of x. This conjecture was later proven and was called the prime number theorem. ”

While muttering softly, Xu Chuan picked up the ballpoint pen in his hand and gently wrote a mathematical formula on the manuscript paper.

【∞∑n=1·1/n^x=∏p（1-1/p^x）。 】

This is a mathematical formula derived from the product formula introduced by Euler, which opens up the possibility of studying integer problems with calculus or real analysis.

However, the difficulty of convergence of the inverter integral at the jump of the π(x) function is the convergence induced by the distance concept given on the function set, so the consistent convergence of the function series is the convergence in the true sense.

"If you want to study the Riemann conjecture from the research idea of regression prime count function π (x), then it is necessary to find this convergence curve function."

"If that's the case, then first deal with Re(s)< Re(a) has (MU{-x^α})=(s+a)."

The corners of his mouth hooked into a smile, and Xu Chuan quickly wrote lines of new mathematical formulas on the manuscript paper.

【(MU{-x^α})·（s）=∫^∞-x^αx^s-1·dx=-∫^∞·x^s+a-1·dx=x^s+a/s+a|^∞.】

Bringing in the Hamada product form, we can get ., from the linearity of the integral, we can know that the Mellin transform is also linear, and the comparison of the above equation gives the following function

The ballpoint pen in his hand depicts one mathematical symbol after another and ancient Greek letters, every number, and even every punctuation mark on the white manuscript paper, which is a precious gift for the mathematical community and for all mankind.

This is the crystallization of wisdom standing at the pinnacle of mathematics, and it is also a proof that the boundaries of human knowledge are once again expanding outward.

In order to allow himself to better study the Riemann conjecture and the π (x) prime number counting function, Xu Chuan has locked himself in the villa at the foot of the Purple Mountain for more than half a month, almost cutting off all contact with the outside world, and devoting himself to this field.

This is the first time since the completion of the 'Unified Framework Theory of Strongly Correlated Electronic Systems' that he has focused all his energy on a single field of mathematics for such a long time.

But the effort paid off, and during this period, he not only perfected the thoughts and ideas in his mind, but also read a large number of papers related to the Riemann conjecture and the π(x) prime number counting function.

He was like a dry sponge, absorbing all the nutrients and knowledge he needed from the papers he had flipped through.

And now, it's all coming together, dripping into the mysterious pond of the Riemann function.

At the beginning of October, the silence of the early morning was broken by the dripping of dew, and the faint light shone through the half-open window on Xu Chuan, who was still immersed in a sea of knowledge.

The ballpoint pen in his hand dropped the last symbol, and Xu Chuan, who was sitting at the desk, stretched his waist, sat up straight from the chair with a yawn, and rubbed his sour and sore waist muscles.

Sensing the faint light outside the window, he picked up his phone from the table and glanced at the time on it, 5:53 in the morning.

At the beginning of October, around six o'clock is about the same time as dawn.

Shaking his head with a smile and putting down his phone, Xu Chuan shifted his gaze to the messy manuscript paper on the table.

There was no doubt that he stayed up all night, but it was totally worth it.

This feeling of total immersion in solving a problem, or expanding the boundaries of knowledge, is so wonderful for a scholar like him.

Unconsciously, his time was stolen little by little.

Sitting back at the desk, Xu Chuan simply sorted out what he had written, and then read it carefully.

After making sure that there was nothing wrong with the calculation he had written, he gathered it together and placed it in the corner of his desk.

This is not a proof of the weak Riemann conjecture, but a tool to prove the weak Riemann conjecture. After regressing the Riemannian function to Janssen's inequality, he further extended it to the π(x) prime counting function.

In the process, he solved most of the problems encountered in solving the weak Riemann conjecture, such as the inverse integral transformation does not converge well at the jump of the π(x) function, and the corresponding L function may have an abnormal zero point outside the above formula when X satisfies special properties.

After these problems are solved, there is only one last step left before the weak Riemann conjecture is left.

However, before solving this last step, he still went to sleep first and recovered the spirit of the night.

PS: There will be a month in the afternoon, ask for a monthly pass, and this certificate should be written out today!