"The zero point problem divides the whole number theory into two universes. The first universe has a zero point, and the second universe does not have a zero point. The question is, which universe do we live in?"

Twenty days after announcing the solution of the Landau-Siegel Zeros Conjecture in advance at the alumni meeting, Chinese-American mathematician Zhang Yitang, a professor of mathematics at the University of California, Santa Barbara, said about the "zero-point conjecture" The online transmission of the paper has been leaked internally.

Zhang Yitang, a Chinese-American mathematician and professor of mathematics at the University of California, Santa Barbara

On the morning of November 5, when Zhang Yitang gave an academic report for the School of Mathematics of Shandong University and other institutions, the screenshots and full text of the above paper were disseminated in WeChat groups such as the alumni group of the School of Mathematical Sciences of Peking University.

Three days later, Zhang Yitang will also give an academic report on the Lang Dao-Siegel Zero-Point Conjecture for the School of Mathematical Sciences of Peking University and the Beijing International Mathematical Research Center.

The PDF file obtained by The Paper (www.thepaper.cn) shows that the full text of the paper has 111 pages and a total of 18 sections, including Introduction, The set Ψ1, Proof of Proposition, etc.

The latest Zhang Yitang paper on Landau-Siegel zero

The title of the paper is Discrete mean estimates and the Landau-Siegel Zero.

The author of the paper is Zhang Yitang, whose name, unit name and e-mail address are attached at the end of the article.

In the acknowledgment section, the paper mentions, "The basic idea of this proof was originally formed when I visited the Institute for Advanced Study in Princeton in the spring of 2014. Thanks to the Institute for providing me with good learning conditions, and thanks to Professor Peter Sarnak encouragement.”

This PDF file was last modified on November 4th at 7:50:53 local time.

But so far, the authenticity of this paper has not been publicly confirmed by Professor Zhang Yitang.

At noon on November 5, some industry experts told The Paper that Zhang Yitang's related papers have been uploaded to relevant websites, "(but) it will take a day or two (before it will be announced to the public)." Whether the proof in the paper is correct remains to be seen. Peer checks in mathematics.

Fifteen years ago, on May 29, 2007, Zhang Yitang submitted a paper titled "On the Landau-Siegel Zeros Conjecture" on the preprint website arXiv. The paper consists of 13 sections and 54 pages. "We provide a proof of a variant of the Landau-Siegel zero-point conjecture," the paper said.

Zhang Yitang's preprint paper "On the Lang Dao-Siegel Zero-Point Conjecture" submitted on May 29, 2007

If its latest paper is also published on the arXiv website, along with the two number theory papers uploaded in 2007 and 2015, there will be three preprint papers signed by Zhang Yitang on the website.

The recipient in the screenshot of the email that sent the latest paper on the Internet is Professor Rick Rugang Ye, a colleague of Zhang Yitang at the University of California, Santa Barbara.

The Paper confirmed that on the morning of the 5th, Professor Zhang Yitang was invited to give an academic report for the School of Mathematics of Shandong University and other institutions, and shared the research results on the Lang Dao-Siegel zero-point conjecture. In addition, the School of Mathematical Sciences of Peking University and the Beijing International Mathematical Research Center also invited Professor Zhang Yitang to give a lecture on November 8th from 9:00 to 10:00 in the morning, "In the Lecture Hall of Buildings A, B and C, No. 82 Jingchunyuan, Peking University (offline) ), zoom online conference, bilibili live broadcast" to conduct an academic report on "Landau-Siegel Zero Conjecture". The screenshot of the paper in the relevant conference notice is the paper that Professor Zhang Yitang will publish on the Internet, titled "Discrete mean estimates and the Landau-Siegel Zero".

A relevant person from Shandong University told The Paper that the above report will be on a small scale. "These results are still in the confidential stage, and we will not release news."

In fact, as early as 20 days ago, at 8:00 am Beijing time on October 15th (8:00 pm EST on October 14th), Professor Zhang Yitang participated in the tenth session of the Peking University Greater New York Alumni Association in New York, USA, "Untitled" Inheritance series of activities", sharing news in advance that the problem of Lang Dao-Siegel's zero-point conjecture has been solved, and related papers will be published. This information has aroused the attention of the domestic mathematics community.

The time for the outflow of the above papers is also consistent with the time previously announced by Professor Zhang Yitang.

According to information released by people close to Zhang Yitang, after participating in the above-mentioned activities in New York, Zhang Yitang and his wife came to Princeton to visit the cemeteries of mathematicians Gödel and von Neumann, as well as the former residence of von Neumann, and then returned to California.

In addition, on October 21, some netizens published a video of Professor Zhang Yitang giving an academic report at CUNY Queens College on the afternoon of the 19th local time, local time.

On the afternoon of November 5, domestic mathematicians posted on social media that today, 67-year-old Zhang Yitang posted his 111-page paper online, saying, "He has made an important breakthrough in the famous Siegel zero-point problem."

The WeChat public account "Lin Kun on Mathematics" released a message saying, "This is a historic moment." "If the article on the Internet today is correct, then Professor Zhang Yitang has solved the famous Riemann conjecture and become today's There is no one of the most outstanding and greatest mathematicians in the world." "The twin prime conjecture and the Riemann conjecture are the most difficult problems in number theory. One person solving these two problems is tantamount to being struck by lightning. Twice." "After mathematicians have done their work and have the results, they usually put it on the Internet so that academic experts can see it. The main purpose is to let people see what you have done and what has been done. , to prevent others from doing repetitive work and wasting precious time and energy. The second is to publish the results and accept the review and questioning of mathematics workers (including the most powerful and authoritative mathematicians) all over the world. Is the content of the article correct? Fatal injury? If it is only a small problem, how to revise it. If it is correct, it will be officially published after it is perfected.”

Cai Tianxin, a professor, doctoral supervisor, and Qiushi Distinguished Scholar at the School of Mathematical Sciences of Zhejiang University, once told The Paper that the Lang Dao-Siegel zero-point conjecture can be said to be a problem related to the generalized Riemann function or conjecture.

The conjecture that asserts that the L function has no anomalous zeros is called the Landau-Siegel conjecture.

On November 16, 2019, Zhang Yitang gave a speech entitled "The Landau-Siegel Zero Point Problem in Number Theory" at the "Future Science Prize Week 2019" in Beijing.

On November 16, 2019, Zhang Yitang gave a speech entitled "The Landau-Siegel Zero Point Problem in Number Theory" at the "Future Science Prize Week 2019" in Beijing. In his speech, he said, "It can now be shown that if such a zero exists, there is at most one. If it exists, it is called a Landau-Siegel zero. Because the two famous mathematicians were the first Start to study this zero. If this zero really exists, then the generalized Riemann hypothesis is wrong. So, in fact, the Landau-Siegel zero problem is to prove that such a zero does not exist." "We To study this zero point problem, we hope to prove that it does not exist." "We dream of proving that it does not exist!" "If this zero point really exists, it is incredible! The generalized Riemann hypothesis is wrong, then what will happen in the universe? We will get a lot of inferences, and very strong inferences, even too strong.”

Zhang Yitang said that some mathematicians said, "The Landau-Siegel zero is a bottleneck in number theory. If it is solved, it will bring a series of inferences, whether in analytic number theory or in algebraic number theory, it is It will have a great impact, and it can be said to be a revolution." At the beginning of the 20th century, many number theorists tried to solve this problem, but they were unsuccessful. Some mathematicians even predicted, "The solution to the Landau-Siegel zero-point problem may be more difficult than the original Riemann zeta function and the original Riemann zeta conjecture."

According to the relevant meeting notice of the School of Mathematical Sciences of Peking University, Zhang Yitang is a 78-level alumnus of Peking University, honorary director of the Min Sihe Number Theory Research Center of Peking University, visiting professor of Peking University, and professor of the University of California, Santa Barbara. He has made mileage in the research of twin prime number conjecture. The breakthrough progress of the card style was invited to give a special report at the 2014 Seoul International Conference of Mathematicians, and won many awards such as the Rove Schock Award-Mathematics Award, the Frank Nelson Cole Award for Number Theory, and the MacArthur Genius Award. .

Zhang Yitang was born in Shanghai in February 1955, and his ancestral home is Pinghu, Zhejiang. Due to his rough life experience and outstanding mathematical achievements, Zhang Yitang is known as a legendary mathematician. He went to study abroad at the age of 30, but was nearly 60 when he published an important paper.

In an article about Zhang Yitang, the Peking University Alumni Network described him as a legendary mathematician who was "down and down half his life".

At the exchange symposium of Peking University’s Greater New York Alumni Association, Zhang Yitang said when answering the question “Does (mathematical research) require extraordinary talent”?

On April 17, 2013, a number theory paper by Zhang Yitang was submitted to the "Annual Mathematics", the most famous publication in the field of pure mathematics. Commented by today's top analytic number theory expert Henry Ivanic: This is an important work with a historic breakthrough, and the article is very beautiful. Thanks to his ice-breaking work on one of the most famous conjectures in mathematics, the twin prime number conjecture, Zhang Yitang went from an obscure university lecturer to the ranks of the world's heavyweight mathematicians.