Zhang Yitang, a Chinese-American mathematician and a professor at the University of California, Santa Barbara
The Paper (www.thepaper.cn) learned that two days after the internal outflow, on November 7, Zhang Yitang, a Chinese-American mathematician and a professor at the University of California, Santa Barbara, made a statement about the Landau-Siegel zero-point conjecture (the Landau-Siegel zero-point conjecture). -Siegel Zeros Conjecture)'s latest paper is officially open to the public on the preprint site arXiv.
Zhang Yitang's latest paper on the Lang Dao-Siegel zero-point conjecture is officially open to the public
The website shows that the above paper was submitted to the website at 15:17 on November 4, 2022 local time. Its PDF file size is 577KB, the full text is 111 pages, and the text is 18 sections, and two theorems have been published.
The title of the paper is Discrete mean estimates and the Landau-Siegel Zero.
Peng Mei News noticed that the title of this paper is only one word different from the theme of Professor Zhang Yitang's academic report at the Faculty of Science and Technology of Keio University in Japan on December 10, 2021. The latter is Discrete mean formulas and the Landau-Siegel zero.
What do international academic peers think of Zhang Yitang's above paper?
On November 6, Fields Medal winner James Maynard (James Maynard) was his Ph.D. tutor, British mathematician dedicated to the field of analytic number theory, and retired professor at the Institute of Mathematics at Oxford University Roger Heath-Brown ( Roger Heath-Brown FRS) told The Paper, "It takes a long time to study this paper, so I can't say whether it is correct yet. But it is clearly written and strategically wise."
For his own proof, Professor Zhang Yitang is full of confidence. More than 20 days ago, at the tenth "Unnamed Inheritance Series Activities" of the Peking University Greater New York Alumni Association held at 8:00 pm on October 14th Eastern Time (8:00 am on October 15th, Beijing time), Zhang Yitang said , "I recently made another major achievement in mathematics. It can be said to be a weaker form, but in essence, it has solved the Landau-Siegel zero (conjecture) problem. Peers in analytic number theory You will know that the solution to this problem may be more meaningful than the twin prime conjecture."
"I can say with certainty that I did it. I know I did it right," Zhang Yitang said in an online report on the campaign.
The Landau-Siegel zero-point conjecture is considered a special and possibly much weaker form of the generalized Riemann conjecture. It asserts that the "Landau-Siegel zero" does not exist. The "Landau-Siegel zero" is defined as a counterexample to the generalized Riemann conjecture.
On the morning of November 5th, Professor Zhang Yitang made an online academic report on the new breakthroughs in the above research to teachers and students of Shandong University.
One day later, at 11:05 a.m. on November 6th, the Shandong University WeChat public account released Lu Guangshi, a professor and doctoral supervisor of the School of Mathematics of Shandong University, the former deputy dean of the School of Mathematics, and the executive dean of the Shandong University Australian National Union College of Science. An article co-authored by Huang Bingrong, a professor at the Institute of Data Science and a doctoral supervisor, and others.
According to the article, Professor Zhang Yitang introduced his innovative ideas in the research of the Landau-Siegel zero-point conjecture, and proved in his latest preprint paper that the real feature L-function of modulo D is in the interval (1−c( log D)^−2024,1] has no real zeros .
"If you replace 2024 here with 1, you will get the Landau-Siegel zero-point conjecture in its original form. Although 2024 is greater than 1, it is not substantially different from 1 in the mathematical sense." Shandong University WeChat public account The above article said.
But does this mean that Zhang Yitang has essentially proved the Landau-Siegel zero-point conjecture? To be confirmed by experts in the mathematics community.
The above article on the WeChat public account of Shandong University stated, “If we believe in the generalized Riemann conjecture, then the Landau-Siegel zero should not exist. The research on the Landau-Siegel zero is very important and is a bottleneck for solving many number theory problems. The so-called Landau-Siegel zero conjecture asserts that the Landau-Siegel zero does not exist. This is an important conjecture in number theory for a long time. Once the Landau-Siegel zero conjecture is proved, many new Breakthrough, simplification and enhancement of many classical number theory results." "The distribution of prime numbers has always been a central issue in number theory research... Just as there is a profound and close connection between the distribution of zeros of the Riemann zeta function and the distribution of prime numbers, the distribution of the zeros of Dirichlet's L-functions It also plays an extensive and fundamental role in prime number theory, and has a profound intrinsic connection with many core issues of prime number distribution, such as Goldbach's conjecture and twin prime number conjecture."
In the lecture at Shandong University, Zhang Yitang and others then conducted in-depth discussions on topics such as the tradition of the Chinese School of Number Theory and the unremitting pursuit of original innovation, the research characteristics and advantages of the Chinese School of Number Theory, and the development of number theory research. Professor Zhang Yitang said that number theory has a promising future at any time. Rigorous academic style and perseverance are very important. Whether the classical method is effective or not depends on whether you can make it to the extreme.
In the above-mentioned activities of the Peking University Greater New York Alumni Association, Zhang Yitang said that solving the Landau-Siegel zero-point conjecture problem ultimately boils down to making an inequality; that is, constructing a set of numbers. "Some people say that the twin prime conjecture is a needle in a haystack. In fact, Landau-Siegel zero is a needle in a haystack. Over the years, I have tried countless (situations), and the numbers have been substituted into it. I have established a whole set of formulas, so I can calculate. I've tried countless situations, and each time it's one ε (sound: ipsilon)."
Zhang Yitang published "Bounded Intervals between Prime Numbers" in Annals of Mathematics on April 17, 2013, and proved for the first time that there are infinitely many pairs of prime numbers (p, q), where the difference between each pair of prime numbers , that is, the distance between p and q, not more than 70 million. This has made breakthrough work for the solution of the century problem "twin prime conjecture", and he has risen from an obscure university lecturer to the ranks of the world's heavyweight mathematicians.
Zhang Yitang, who was looking for a needle in a haystack to solve the Landau-Siegel zero-point conjecture, said that he searched the "bottom of the sea" and finally found that the zero-point conjecture could be solved without this needle.
He said, "The earliest Dirichlet began to study this problem in 1837, and it has been nearly 200 years... It is always one ε (sound: Epsilon), and it is still impossible to break through. But it should be said, I still broke through. , and finally I made it work."
Zhang Yitang's latest paper, which was leaked internally in advance, was also hotly discussed by netizens on the well-known social forum Reddit. On the well-known mathematical interactive website mathoverflow, some netizens asked, assuming Zhang Yitang's proof is correct, then, what famous number theory results will there be next?
The WeChat public account "Prince Tiger Team" quoted relevant sources as saying that Zhang Yitang's colleague once said that "if Zhang Yitang can prove the Landau-Siegel zero-point conjecture, it is equivalent to a person being struck by lightning twice". Number theory expert Jeffrey Stopple pointed out that Zhang Yitang's results can be used to study a problem left over by Euler and Gauss about the "idoneal number" (idoneal number), and turn it into a finite number of calculations. Of course, everything is based on the fact that Zhang Yitang's paper is correct.
At the "Future Science Prize Week 2019" in Beijing, Zhang Yitang said that in many research areas, because we don't know whether the Lang Dao-Siegel zero exists or not, number theorists have to discuss two situations: if it Existence, what conclusions can be drawn? If it didn't exist, what would be the conclusion? "If this zero point really exists, it's incredible! The generalized Riemann hypothesis is wrong... We will get a lot of inferences, and they are very strong inferences, and even a little too strong."
Fifteen years ago, on May 29, 2007, Zhang Yitang submitted a paper titled "On the Landau-Siegel Zeros Conjecture" on the preprint website arxiv, saying, "We provide provides a proof of a variant of the Landau-Siegel zero-point conjecture." But there are said to be problems with the proof process.
This time, people hope that Zhang Yitang will make another important breakthrough in mathematical research.
Peking University, Peking University School of Mathematical Sciences, Beijing International Mathematical Research Center and other WeChat public accounts announced on the afternoon of November 5 that Professor Zhang Yitang was invited and will conduct an online "" An academic report on the Landau-Siegel zero-point conjecture".
