Chapter 682: The ‘freak’ who is different from ordinary people
In the villa at the foot of Purple Mountain, Xu Chuan was obsessed with studying the Riemann Hypothesis.
Although it is said that he has found a way to the weak Riemann Hypothesis, it is still unknown whether he can ultimately solve this problem.
Moreover, even if this idea is effective and can continue to advance the critical zone of the Riemann Hypothesis, it is not easy to continue to narrow and solve it.
Mathematicians often write the real part and imaginary part of the non-trivial zero point of the Riemann zeta function as σ and t respectively, and put 0 0.35N on the complex plane. It is controversial that No(T) was previously proved by Professor Walter Jeffrey of Harvard University.
>0.4N, which step have you achieved?"
Although the Riemann Hypothesis is not in his current research scope, as a scholar who has solved the Weil Hypothesis (Riemann Hypothesis on elliptic curves), he is naturally aware of the current progress of the Riemann Hypothesis in mathematics.
The idea of squeezing the critical band is the most commonly used and effective proof method in today's mathematics world. Xu Chuan used this method to study the Riemann Hypothesis, which was not surprising to him.
On the opposite side, Xu Chuan shook his head and said: "The idea of continuing to compress the critical zone is indeed feasible, but I am not prepared to do so."
Hearing this, Deligne's face suddenly showed a surprised look: "How do you say that?"
After thinking for a while, Xu Chuan said: "Intuition, right?"
After a slight pause, he continued: "In recent days, I have read a lot of research and papers on the Riemann Hypothesis, and many of the results are based on the idea of compressing the critical band."
"It is undeniable that these results are indeed outstanding. But in my personal opinion, it is too difficult to compress the Riemann zeta function and non-trivial zero points to the number 1/2. Or, it can even be done
Said there was no hope."
"After all, prime numbers are infinite, and the number of non-trivial zero points is also infinite. This point alone is enough to block the current research ideas of compressed critical bands."
"It may be possible to continue on this path, and even push it to 0.45, 0.46 or even higher, but I don't think there is much hope of stably compressing it to 1."
"At least there is little hope with current traditional research methods."
For Xu Chuan, reading the papers these days is not in vain.
Although there wasn't much that was helpful, he knew quite clearly about methods to compress the critical band and increase the number of non-trivial zeros on the critical band.
Intuition told him that although this method is very effective in studying the Riemann Hypothesis, if he wants to rely on it to solve the Riemann Hypothesis and push the real root of the non-trivial zero point to 1/2, the feasibility is almost zero.
Otherwise, he does not need to find another way to find another method, he can just continue the previous research.
Listening to Xu Chuan's explanation, Deligne frowned, with some contemplation on his face.
By compressing the critical band and increasing the number and proportion of non-trivial zeros on the critical band, this method is one of the mainstream methods in the current mathematics community to study the Riemann Hypothesis, and it can even be said to be the mainstream method.
After the 21st century, more than two-thirds of the research on the Riemann Hypothesis is based on this method.
But even counting the controversial No(T)>0.4N from Harvard University, they are actually far away from the ultimate goal of No(T)=N(T) (that is, all non-trivial zero points are on the critical line), and
There is still a long way to go.
0.4-N(T), or 0.4-1, which is still a difference of 0.6.
Over the past century and a half, their progress can even be described as insignificant for the Riemann Hypothesis.
But in any case, compressing the critical band and increasing the number and proportion of non-trivial zero points on the critical band is still the best way to study the Riemann Hypothesis at present.
However, Xu Chuan now says that he is not prepared to use the traditional method of compressing the critical zone to study the Riemann Hypothesis, and even speculates that this research route may not work.
Although he stood at his height, he would rarely have his heart shaken by one or two unproven opinions, but this time he was indeed surprised by his own student.
Taking a deep breath, Deligne quickly said: "If it's convenient, can you tell me your research ideas?"
In academia, asking for research ideas from a scholar who is researching a difficult problem is a taboo thing, even if this person is his student.
But at this moment, Deligne didn't care about these things anymore.
After all, this is the Riemann Hypothesis, which is related to thousands of mathematical theorems!