In the office, Xu Chuan clicked on the link handed over by Xiao Ling with interest and downloaded the paper in the email.

When he saw the title of the paper, he raised his brows, with a look of interest in his eyes.

"New Big Value Estimation Based on Dirichlet Polynomial"

The title of the paper is very simple, but there is no such simple thing when it comes to research on Riemann's conjecture.

Dirichlet-polynomial distribution is a probability distribution, which is the promotion of polynomial distribution. This mathematical tool is generally widely used in probability theory and statistics, and is often used in natural language processing, text mining and other fields.

For example, the latent Dirichlet allocation (lda) algorithm used in thematic model. It also plays an important role in Bayesian statistics and is used to describe multiple categories of random variables.

In addition, it is also used to describe the probability distribution of multiple mutually exclusive and discrete results in an experiment.

For the Riemann conjecture, the Dirichlet polynomial boundary plays an important role in several problems related to the distribution of prime numbers.

Simply put, they can be used to limit the number of zeros in the Riemann zeta function in a vertical strip, which is related to the distribution of prime numbers in short intervals.

That is, the Dirichlet polynomial can be expressed as: "D(t)=\sum_{n = N}^{2N} b_n n^{it}."

But to be honest, using this tool to study the Riemann conjecture is not a very novel thing.

As early as decades ago, mathematician Professor Albert Ingham used this tool to make substantial improvements to the classical boundaries about the zero points of the Riemann zeta function and the wider control of the large values ​​of various Dirichlet series in 1940.

However, in the following decades, the inferences about the Riemann conjecture were limited to this and there was no breakthrough.

Therefore, Xu Chuan is still looking forward to the paper in his hand.

This may provide him with some value in the research of Riemann's conjecture.

After all, if it is not valuable, the editor-in-chief of "New Progress in Mathematics" will not be able to send the paper to him personally and invite him to review the manuscript.

In the office, Xu Chuan quickly downloaded the paper and sent it to the printer, ready to print it out.

Compared to reading papers directly on the computer screen, he prefers paper manuscripts.

Before that, he clicked on the paper on his computer and couldn't wait to browse it.

"...It's interesting. The first part of this paper was actually done based on Fourier analysis, but it is not a traditional stationary phase method."

"But based on the new frequency limit of the Dirichlet polynomial to take the maximum value, the zero-point boundary of the Riemann ζ function given by Ingham is substantially improved..."

Reading the paper in hand, Xu Chuan's eyes were full of interest and thought.

I have to say that this is indeed a very clever method.

The most important part for expressing Riemann functions using Dirichlet polynomials is the size of the D (t) superlevel set.

The authors of this paper normalize so that the coefficient norm is up to 1, and then study the super-level set | D (t)|> N^\sigma, where the sigma index is between 1/2 and 1.

This alone is enough to reflect the wonderful aspects of this paper.

While flipping through the paper, Xu Chuan muttered softly.

A paper has a wonderful enough place, which is enough for people like him.

"Professor, your printed paper is ready."

Just as Xu Chuan was immersed in the paper, someone gently knocked on the door of the office twice. Assistant Lu Ling hugged a stack of papers in her hand and walked in quickly.

"Give it to me."

Xu Chuan reached out to take the paper without hesitation, and ignored Lu Ling.

Just as he was about to learn more about this paper, he suddenly remembered another thing and shouted.

"Xiao Ling, please help me reply an email to Professor Robert Morey Dean, editor-in-chief of "New Mathematics", and said that I was invited to accept the review."

In the lower right corner of the display, a chat box that was originally hidden popped up.

"Received, Master!"

"Email reply!ヾ(≧▽≦*)o"

At the same time, at the door of the office, Lu Ling, who was about to turn around and go out, was stunned for a moment when she heard the sound and stopped.

She turned her eyes to Xu Chuan in surprise and confusion.

Is this...instructing her?

But she is not called Xiaoling, and the professor seems to have never called her that.

After hesitating for a moment, Lu Ling decided to ask, after all, what if the professor gets up and shouts more intimately?

"That... Professor, did you just ask me to send an email to the editor-in-chief of "New Progress in Mathematics"?"

Hearing the sound, Xu Chuan replied without raising his head: "I didn't call you, I'm talking to others, it's okay."

Lu Ling was a little confused, but she replied: "Okay, if you need anything, just tell me."

While replying, she also looked at the entire office.

In broad daylight.

Who is the professor talking to?

If you didn't call her, who did you call me?

Could it be that this is...haunted?

Thinking of this terrible possibility, Lu Ling couldn't help but shivered.

Although as an assistant to a great scientist, she should not believe in such things as metaphysics.

But she has been afraid of ghosts since she was a child.

It was daytime, and there was no one else in the office, but the professor was talking to others. This...it was so scary...

After muttering, Lu Ling walked out quickly.

"Tang Ran, Tang Ran. Let me tell you, maybe it's haunted in the professor's office?"

When he got to another assistant, who is now his best friend, Lu Ling said in a low voice.

In the assistant office, Tang Ran, who was sorting out the information, was stunned and looked at the good sister suspiciously.

"What's wrong with you? Being possessed by evil?"

While saying that, she reached out to test Lu Ling's forehead, trying to see if she had a fever, but she was so hot that she started talking nonsense.

Lu Ling patted her hand off and quickly whispered: "To be honest, the professor just talked to people in the office and even ordered work. But there were no other people in his office."

"Isn't this haunted, what's it?"

Hearing this, Tang Ran was so amused that he was so angry that he pushed her head with his fingers and said, "What is the one in your mind?"

"This is the professor's office, how can something like haunted happen?"

"But...but there is really no one else in the professor's office." Lu Ling added quickly.

Tang Ran said helplessly: "Maybe the professor is chatting with others? You are an assistant to a great scientist and believe in haunted things. You are not afraid of jokes when you tell them."

Lu Ling muttered, and Tang Ran was helpless and said, "Okay, it really doesn't work. After the professor gets off work, would you please ask him?"

.........

In the office, Xu Chuan didn't know that the tasks he arranged for the AI ​​assistant were treated as him talking to the ghost.

Now he has been immersed in the paper in his hands.

Although "New Progress in Mathematics" was sent to him, the paper invited to serve as reviewer was not long, only a dozen pages long.

But it has to be said that this paper has indeed opened up a new direction in the research of the Riemann conjecture.

The size of the D (t) superlevel set is normalized so that the coefficient norm is up to 1. Then, study the superlevel set|D (t)|>N^\sigma, and improve the sigma boundary from 1/2 to close to 3/4.

In addition, the paper also discusses existing simple estimation methods and their limitations by analyzing the new boundaries of the Dirichlet polynomial maximum and the size of the Dirichlet polynomial norm on a specific set.

These studies are of great significance in analytical number theory, and have made new tools for the study of Dirichlet function on the size of a specific set, which can solve similar problems more cleverly and simply.

What makes Xu Chuan regret is that this paper does not promote much of the Riemann conjecture.

In other words, this paper only re-advances the distribution of non-trivial zero points of the Riemann function through another route on the original basis.

But he was still a little far from proof of the weak Riemann conjecture he had completed, and did not break the limit he set.

This is also something that Xu Chuan feels regretful.

......

After carefully seeing the paper from the beginning and carefully reviewed it. After confirming that there were no problems, Xu Chuan turned on the computer, wrote down his review opinions at the end of the paper, and marked the four words "pass review".

Generally speaking, reviewing papers is a relatively tedious task.

Even for ordinary papers, in most cases, it takes three to five days or even a little longer to complete the manuscript.

After all, for the academic community, rigor is the most important spirit. Ensuring the correctness of the paper review is the basic principle for every invited professor to review.

For papers related to the Millennium Problem, the review time will only be longer.

However, for Xu Chuan, a paper of this level can basically be found by reading it carefully.

But he still carefully reviewed it twice out of his academic rigor.

After asking Xiaoling to send the approved email to "New Progress in Mathematics", Xu Chuan picked up the paper paper printed on the desk again.
To be continued...