Great Country Academician

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

After saying hello to Zheng Hai, he huddled in his study and studied with concentration.

He already had preliminary ideas on the research on the weak Riemann Hypothesis, and there was no reason why he should not continue to study it.

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

For Xu Chuan, it has been a long time ago that he devoted himself wholeheartedly and long to the research of a mathematical conjecture.

If we really want to trace it back, we probably have to go back to the completion of the ‘Unified Framework Theory of Strongly Correlated Electronic Systems’.

And in the follow-up, whether it was the research on the Yang-Mills existence and mass gap problems, or the research on issues such as Einstein's Rosen Bridge, it actually did not take him a long time or devote himself to it.

The former is the result of research in a previous life. Even the second method of verifying the quality gap is nothing more than a sudden inspiration on the lecture desk, and it is just a follow-up.

As for Einstein's Rosen Bridge, there is no need to say more. So far, he has only scratched the surface of this problem.

Today, the research on the Riemann Hypothesis has allowed him to devote all his energy to it.

However, this feeling is not unfamiliar to him. Even when he fully enters this field, the feeling of mathematics is like the 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 seemed as if the whole world had disappeared, leaving only the Arabic numerals and ancient Greek symbols in front of him.

The pen slides smoothly across the paper, leaving wonderful characters one after another, as if every stroke is a poem, and every word is a bright star, lighting up the whole world.

Late at night, a gentle lamp lights up in the quiet study, and the Purple Mountain outside the window seems to be sleeping. Occasionally, there are some rustling sounds, just like love words in a dream.

Staring at the manuscript paper on the desk, Xu Chuan's eyes were bright and he muttered softly.

"The zero points of Reimann ζ are inseparably related to prime numbers. The most direct one is that the prime number counting function π(x) can be represented by the zero points of ζ. The prime number counting function gives the number of prime numbers less than or equal to x."

"In order to infer the law of π(x), both Gauss and Legendre have done a lot of numerical calculations. They respectively guessed that when x→∞, π(x) x/ ln x, where "" represents two The ratio of functions tends to 1, ln x is the natural logarithm of x. This guess was later proved, and people called it 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 obtained after the product formula introduced by Euler, which provides the possibility to study integer problems using calculus or real analysis.

The difficulty in converging the inverse integral at the jump point of the π(x) function is the convergence induced by the distance concept given to the function set, so the consistent convergence of the function sequence is convergence in the true sense.

"If you want to study the Riemann Hypothesis from the perspective of regressing the prime counting function π(x), it is necessary to find this convergence curve function."

"If this is the case, then first deal with (MU{-x^α}) = (s+a) for Re(s) \u003c Re(a)."

With a smile on his lips, Xu Chuan quickly wrote down new mathematical formulas line by line 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. Comparing the above formula, we can get the following function

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

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

In order to better study the Riemann Hypothesis and the π(x) prime number counting function, Xu Chuan has locked himself in a villa at the foot of Purple Mountain for more than half a month, almost cutting off all contact with the outside world. , devoted full attention 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 certain field of mathematics for such a long time.

But the effort paid off. During this period, he not only perfectly sorted out the thoughts and ideas in his mind, but also read a large number of papers related to the Riemann Hypothesis and 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 read.

But now, they are brought together and dripped into the mysterious pond of the Riemann function.

In early October, the silence of the early morning was broken by the sound of dripping dew. The faint light passed through the half-open window and fell on Xu Chuan, who was still immersed in the ocean of knowledge.

The ballpoint pen in his hand dropped the last symbol. Xu Chuan, who was sitting in front of the desk, stretched, yawned and sat up straight from the chair, rubbing the sore and painful waist muscles.

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

In this season and time of early October, it’s almost dawn around six o’clock.

Shaking his head with a smile and putting down his phone, Xu Chuan turned his attention to the scattered manuscript papers on the table.

No doubt he had to stay up all night again, but it was totally worth it.

This feeling of being completely immersed in solving a certain problem, or in other words, expanding the boundaries of knowledge, is simply too wonderful for a scholar like him.

Unconsciously, the time that belonged to him was stolen bit by bit.

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

After confirming that there were no problems with the calculation process he had written, he gathered it together and placed it in the corner of the desk.

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

In this process, he solved most of the problems currently encountered in solving the weak Riemann Hypothesis. For example, the inverse integral transformation cannot converge well at the jump of the π(x) function. For example, when X satisfies special properties, its The corresponding L function may have abnormal zero points that fall outside the above formula, etc.

After these problems are solved, there is only the last step left to the weak Riemann hypothesis.

However, before solving this last step, he should go to sleep first and recover his energy after staying up all night.

PS: There will be more in the afternoon. Please vote for me. I should finish writing this proof today!