Chapter 399: 3 World-Class Mathematical Conjectures, Can You Still Beat Me?

Xu Qingzhou's life was fulfilling; listening to lectures, going to the library to read materials, or going home to do calculations.

Except for the stronger academic atmosphere and the fact that the people around him had basically become foreigners, his life didn't seem to have changed.

Still in free-range mode.

During this period, a major event happened in the mathematical world.

Young mathematician Jerry Bronson proved the Strong Mersenne Conjecture.

After Xu Qingzhou finished reading the other party's introduction, he exclaimed, "Good guy."

Introducing Hodge theory into combinatorics, proving the Dowling–Wilson conjecture of geometric lattices, proving the Heron–Rota–Welsh conjecture of matroids, and developing Lorentz polynomials.

There are at most four people for the Fields Medal, so the academic world had already started predicting the winners of the 2018 Fields Medal.

The hottest candidate was naturally Xu Qingzhou himself.

Cramér's conjecture, Twin Prime conjecture, Polignac's conjecture...

The second was young mathematician Jonathan Birmingham, who proved the exponential ergodicity of solutions under the 1-Wasserstein distance and proposed a criterion for the exponential ergodicity of Markov semigroups on Banach spaces under the 1-Wasserstein distance.

The third was this Jerry Bronson.

Xu Qingzhou didn't have much pressure.

I have three world-class mathematical conjectures in hand; can you still beat me?

Unless someone directly knocks out two Millennium Prize problems within this year, overwhelmingly crushing them all, otherwise, the Fields Medal would definitely have his name.

On July 26th, Professor Roberts returned from New York after attending a seminar, and Xu Qingzhou was also preparing to go to the office.

Passing by the iconic Great Dome of MIT, one could see students sitting idly and sunbathing outside the Stratton Student Center, and there were also nearby residents camping on the lawns along the way.

Compared to this, there wasn't much of the sense of urgency felt when walking on the roads of Jingda.

Just speaking of the academic atmosphere, one could still clearly feel the gap between domestic and foreign countries.

MIT is not big, and compared to some 985 universities in the country, it can even be said to be a bit miniature, but such a school makes a large number of students flock to it.

"Domestic... the future will get better and better."

Xu Qingzhou had great confidence.

He secretly sighed again; sure enough, the status of Shuimu and Jingda in the hearts of Xia Nation people is the same as the status of A-shares in the hearts of retail investors.

Just as Xu Qingzhou arrived downstairs at the Mathematics Department, he suddenly saw a somewhat familiar figure, and the other party was smiling and waiting for him.

He looked at the handsome man in a suit in front of him and was stunned for a moment. "You are... Holn?"

"Hi, Xu, see you again." Holn waved his hand.

Xu Qingzhou was very surprised. If it weren't for the somewhat similar body shape, he absolutely wouldn't have recognized him. Now, after tidying up a bit... you know, the fat version of Thor.

No wonder this guy said women are very enthusiastic...

Surprise aside, he still corrected: "It's Xu, not *Xu* (pronounced like 'empty')."

"Your Xia Nation's Chinese is really too difficult."

Holn sighed, paused, and said: "Okay, Xu, after it's over, do you want to go for a drink? I just happen to have a friend to introduce to you... your fan, oh."

Xu Qingzhou gave up explaining that he wasn't *Xu*.

He said helplessly: "Sorry, I have other arrangements tonight, I'm afraid I don't have time to drink with you."

Holn shrugged regretfully and didn't insist. While walking, he asked: "Your Riemann Hypothesis... is it going well?" "I have some general research directions."

Xu Qingzhou sighed and said, the Riemann Hypothesis is worthy of being one of the seven Millennium Prize problems; it is harder than the problems he had encountered before. It is very tricky, and it can be said that the beginning is difficult, the middle is arduous, and the end... still can't see the end.

Professor Roberts is good at the study of number-theoretic functions, and he happens to have several function problems on integer sets here.

"Amazing, I tried it at the beginning, but I gave up after only a week." Holn clicked his tongue.

The Riemann Hypothesis is like a hidden treasure in the mathematical kingdom. Countless wise men have spent their whole lives exploring its whereabouts, but its mysterious veil has yet to be lifted.

The most critical thing is that this treasure is nakedly placed in front of everyone, just telling you: I am right here, as long as you can find the way.

Holn glanced at the young face beside him.

Although this Xu Qingzhou had already created several miracles, if the opponent is the Riemann Hypothesis, it is difficult to have a chance of winning.

Professor Roberts was flipping through a stack of manuscripts. Seeing Xu Qingzhou enter, he greeted Xu Qingzhou to sit down and stuffed the manuscripts onto the bookshelf on the side.

The office was still the same as before, giving people an unfathomable feeling amidst the mess.

(Author's note: Read every word of the content!)

Xu Qingzhou greeted him and stated his current train of thought.

"Inequality? The Landau-Siegel zero conjecture. That's a good line of thought." Professor Roberts pondered for a moment and nodded slightly.

Xu Qingzhou continued: "Then construct a mathematical structure related to the existence of Landau-Siegel zeros through inequalities... Next, use the introduced inequalities and mathematical models to reason."

As for why Xu Qingzhou suddenly thought of Landau-Siegel zeros, it is necessary to first talk about the Dirichlet L-function.

Professor Maynard and the others proved a new bound for the frequency of large values of Dirichlet polynomials.

The reason this thing is important is that if the Dirichlet character χ(n) is taken as the trivial character that is always equal to 1, then the Dirichlet L-function becomes the Riemann Z-function.

Moreover, the Generalized Riemann Hypothesis is a generalization of the Riemann Hypothesis, which asserts that the real parts of all non-trivial zeros of the Dirichlet L-function are equal to 1/2.

Going further, it is the Landau-Siegel zero related to the Dirichlet L-function.

Xu Qingzhou's idea is very simple: first solve the Landau-Siegel zero problem.

The Riemann Hypothesis is a conjecture about the distribution of zeros of the Riemann Z-function, while the Landau-Siegel zero problem is a special case of the Generalized Riemann Hypothesis, or a special zero related to it.

This zero is conjectured to possibly exist at certain special positions of the Dirichlet L-function.

If a Landau-Siegel zero exists, then the Riemann Hypothesis is wrong. Conversely, if a Landau-Siegel zero does not exist, it will not conflict with the Riemann Hypothesis.

For Xu Qingzhou's idea, Professor Roberts and Holn both expressed praise, but they were not too surprised, because no matter how you look at it, it is still looking for a needle in a haystack.

Over the past hundred years, many mathematicians have proposed corresponding solutions, but in reality...

Xu Qingzhou didn't care; at least there was a specific range. At worst, he would really find a way to search the seabed.

After expounding his plans, he also took out the manuscripts and asked Professor Roberts for advice on several difficult problems he had encountered during this period.

After Xu Qingzhou came out from Professor Roberts' side, it was about 6:30 PM. He took a taxi to a ring shop called "Cartier" in downtown Boston.

School Beauty Song's birthday was on the 5th of next month. He had to get the gift back in advance. This was a pair of white couple rings booked ten days ago, engraved with the names of Xu Qingzhou and Song Yao.

(End of chapter) ===== CHAPTER 400 =====