Chapter 831 The Fastest Review in History

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

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

"New Large Value Estimation Based on Dirichlet Polynomials"

The title of the paper is simple, but when it comes to the study of the Riemann hypothesis, it is not that simple.

The Dirichlet-multinomial distribution is a probability distribution, which is a generalization of the multinomial 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 topic models. It also plays an important role in Bayesian statistics, used to describe multi-category random variables.

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

For the Riemann hypothesis, the Dirichlet polynomial bound plays an important role in several problems related to prime number distribution.

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

That is: Dirichlet polynomials 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 hypothesis is not a very new thing.

As early as decades ago, mathematician Professor Albert Ingham used this tool in 1940 to make substantial improvements on the classical bounds on the zeros of the Riemann zeta function and more broadly control the large values ​​of various Dirichlet series.

However, in the following decades, the inferences about the Riemann hypothesis were limited to this, and there has been no breakthrough.

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

This may provide some value for his research on the Riemann hypothesis.

After all, if there is no value, the editor-in-chief of "New Advances in Mathematics" would not personally send the paper to him and invite him to review it.

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

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

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

".It's interesting that the first part of this paper is actually based on Fourier analysis, but it does not use the traditional stationary phase method."

"It is based on the new frequency limit of the large value of the Dirichlet polynomial, which substantially improves the zero point limit of the Riemann zeta function given by Ingham."

Reading the paper in his hand, Xu Chuan's eyes are full of interest and thinking.

It must be said that this is indeed a very clever method.

For using Dirichlet polynomials to express Riemann functions, the most important part is the size of the D (t) super level set.

The author of this paper normalizes so that the coefficient norm is at most 1, and then studies the super level set | D (t) |> N^\sigma, where the sigma index is between 1/2 and 1.

This alone is enough to show the wonderfulness of this paper.

Flipping through the paper, Xu Chuan muttered softly.

A paper with one wonderful enough point is enough for people like him.

"Professor, your printed paper is ready."

Just as Xu Chuan was immersed in the paper, the door of the office was knocked twice, and assistant Lu Ling walked in quickly with a stack of papers in her hands.

"Give it to me."

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

Just as he was about to take a deeper look at this paper, he suddenly remembered another thing and shouted.

"Xiao Ling, help me reply an email to Professor Robert Morey Dean, the editor-in-chief of "New Advances in Mathematics", saying that I accepted the invitation to review."

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

"Received, Master!"

"The email has been replied!ヾ(≧▽≦*)o"

At the same time, at the door of the office, Lv Ling, who was about to turn around and leave, was stunned for a moment after hearing the voice and stopped.

She looked at Xu Chuan with some surprise and doubt.

Is he ordering her?

But her name is not Xiao Ling, and the professor seems to have never called her that.

After hesitating for a while, Lv Ling decided to ask, after all, what if the professor got excited and called her more intimately?

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

Hearing the voice, Xu Chuan replied without raising his head: "I didn't call you, I was talking to someone else, it's okay."

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

While replying, she also looked around the entire office.

In broad daylight.

Who is the professor talking to?

He didn't call her, who should he call?

Could it be that this is haunted?

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

Although as an assistant to a great scientist, she shouldn't believe in metaphysics.

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

In broad daylight, there was no one else in the office, but the professor was talking to someone else. This... This is too scary

Muttering to herself, Lv Ling walked out quickly.

"Tang Ran, Tang Ran. I tell you, the professor's office may be haunted?"

Lv Ling whispered to another assistant, who is now her best friend.

In the assistant's office, Tang Ran, who was sorting out documents, was stunned and looked at her good sister with suspicious eyes.

"What's wrong with you? Are you possessed?"

While saying this, she reached out to test Lv Ling's forehead to see if she had a fever, and she started talking nonsense because of the fever.

Lv Ling slapped her hand away and whispered quickly, "I'm serious, the professor just talked to someone in the office and even gave instructions. But there's no one else in his office."

"If this isn't a haunted place, what is it?"

Hearing this, Tang Ran didn't know whether to laugh or cry. He pushed her head with his finger and said, "What's in your head?"

"This is the professor's office. How could there be a haunted place?"

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

Tang Ran said helplessly, "Maybe the professor was chatting with someone else? You're an assistant to a great scientist, and you believe in haunted places. Aren't you afraid of being laughed at if you tell others about it?"

Lv Ling muttered to herself, and Tang Ran was helpless, saying, "Okay, if it doesn't work, why don't you ask the professor after he gets off work?"

In the office, Xu Chuan didn't know that the task he casually assigned to the AI ​​assistant was taken by his assistant as him talking to a ghost.

At this time, he was already immersed in the paper in his hand

Although the paper sent to him by New Advances in Mathematics and invited him to serve as a reviewer is not long, it is only a dozen pages long.

But it must be said that this paper has indeed opened up a new direction in the study of the Riemann hypothesis.

The size of the D (t) super level set is normalized so that the coefficient norm is at most 1, and then the super level set | D (t)|> N^\sigma is studied, and the sigma limit is improved from 1/2 to nearly 3/4.

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

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

It's just that Xu Chuan regrets that this paper does not make much progress in the Riemann hypothesis.

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

But there is still a long way to go before he can prove the weak Riemann hypothesis, and he has not broken through the limit he set.

This is also what Xu Chuan regrets.

After reading the paper carefully from beginning to end and reviewing it carefully, and confirming that there are no problems, Xu Chuan turned on the computer, wrote his review comments at the end of the paper, and marked it with the words "passed review".

Generally speaking, the review of a paper is a tedious task.

Even for ordinary papers, in most cases, the review will take three to five days or even longer to complete.

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

For papers related to the Millennium Problem, such as the Riemann Hypothesis, the review time will only be longer.

However, for Xu Chuan, for papers of this level, basically a careful look can find out the possible papers.

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

After asking Xiao Ling to send the approved email to New Advances in Mathematics, Xu Chuan picked up the printed paper on the table again.

For a good paper, even if you understand it, it does not mean that the value in it has been completely squeezed out.

It is like a cup of good tea, which can be tasted repeatedly.

At this moment, his mobile phone on the desk vibrated, and the ringing sound rang in the office.

Picking up the phone, Xu Chuan took a look. The person who called him was Professor Robert Morey Dean, the editor-in-chief of New Advances in Mathematics, to whom he had just replied.

Knowing what the other party wanted to talk to him about, Xu Chuan did not hesitate and answered the phone directly.

"Hello, Professor Xu, I am Robert Morey Dean, the editor-in-chief of New Advances in Mathematics."

The voice of a middle-aged man came from the other side of the phone.

Xu Chuan smiled and said, "Hello, Mr. Robert."

"I hope I didn't disturb your research work by calling you."

Robert Morey Dean smiled and said, "It's like this. About two hours ago and about ten minutes ago, I received your emails accepting the review and passing the manuscript review."

"I want to consult you."

Hearing the hesitation coming from the phone, Xu Chuan smiled, knowing what he was worried about, and said: "Don't worry, I have some time this afternoon. I have carefully reviewed the paper and there is no problem."

Hearing this explanation, Robert hurriedly said: "Please don't get me wrong, I don't doubt your academic credibility, I am just surprised by such a fast speed."

After a pause, he continued with a smile: "Since I became the editor-in-chief of "New Advances in Mathematics", I have reviewed many papers, but only Professor Xu can complete the paper review in just two hours."

"If you are willing to apply for the Guinness record, this will definitely achieve the academic record of 'the fastest review in history'!"

Xu Chuan smiled and said: "Forget about applying for the Guinness record. This is just that I happened to encounter the field I am good at. I happened to be studying the Riemann hypothesis recently, and I just happened to have some time."

Hearing this, professionalism made Professor Robert quickly say: "Are you studying the Riemann hypothesis recently? Then can I make an appointment with you in advance to submit the paper?"

Hearing the paper appointment, Xu Chuan couldn't help but move the corners of his mouth. Come again?

This is how the editor-in-chief of New Advances in Mathematics got the proof of the NS equation out of his hands, resulting in the interim results and final proof of the NS equation being split into two different journals.

Although this is not a big deal, for someone like him who has a bit of obsessive-compulsive disorder, it is a bit uncomfortable to not submit the interim proof and final proof of a problem to the same journal.

"Ahem." After a light cough, Xu Chuan said, "It's just some research, and there is no progress at present."

Robert quickly replied, "It doesn't matter, we can wait for your news at any time."

Xu Chuan: "Let's talk about it later, the Riemann hypothesis is not such an easy problem to solve."

Robert smiled: "Okay, OK, then contact me later. If there is anything that our New Advances in Mathematics can help with, please let Professor Xu know."

After hanging up the phone, Xu Chuan couldn't help shaking his head.

Not to mention that it is impossible to predict how long it will take to prove the Riemann hypothesis. Even if he is lucky enough to solve this problem this time, he will not be able to submit related papers to other journals.

Don't forget that his Hope is still being established and is still crying out for food.

How could he leak such a top-notch paper?

PS: Please vote for the second update, and there will be another update in the afternoon.