Chapter 435: The Wedding

"Song Yao, taking a shower..."

Sure enough, Xu Shouyun and Wang Xiaping called, saying they were going back to their hometown to attend a cousin's wedding.

"How are Grandpa and Grandma?"

Xu Qingzhou asked, leaning on the sofa.

"Oh, that's good... we're all doing well too."

These days, he received quite a few emails, mostly related to the Riemann-Siegel zero hypothesis.

For example, Fields Medal winner Professor Juraj Milton sent several modification suggestions; some formulas could be slightly reduced.

Others were extended research on the Riemann-Siegel zero problem.

Among them, the one that caught Xu Qingzhou's attention most was Zhang Yitang's twelve-page paper.

Zhang Yitang's proof approach was similar to his. There was no doubt that if it weren't for a "cheat" like him, the most cutting-edge researcher of the Riemann-Siegel problem should be this person.

Xu Qingzhou saved these emails and replied to them one by one to express his gratitude.

The sound of the bathroom water disappeared. Song Yao came out, and as the temperature rose, she had changed into summer pajamas, the hem revealing two slender legs.

Xu Qingzhou was a bit greedy.

Song Yao tilted her head, using a towel to rub her hair: "Uncle and Auntie's call?"

"Mm, going back to the hometown these few days, attending a wedding of an old brother of mine."

Xu Qingzhou held the hair dryer and signaled Song Yao to sit down.

After more than ten minutes, the sound of the hair dryer disappeared.

"Ding~"

Xu Qingzhou's phone rang with a series of message sounds.

Wang Xiaping's message.

It was photos of the wedding, and videos.

"Really quite lively."

The two huddled together.

"However, compared to this, I think ours can use Chinese style."

Xu Qingzhou touched his chin. Song Yao's figure, wearing a phoenix coronet and robes, would absolutely be beautiful.

"Mm," Song Yao nodded in agreement, but then felt something was wrong, and said proudly: "Hmph, haven't said I'm marrying you yet."

"It's the same if you marry me."

Xu Qingzhou said gloomily: "With your martial power, if placed in ancient times, you would definitely have beaten me unconscious and dragged me home."

Song Yao gave this person a claw on the waist, rested her chin on her hand and watched the wedding video, actually yearning for it. "At that time, we can take a few sets of Chinese and Western style. The wedding will be Chinese style... but that's at least after we graduate."

Marriage and such, it's still appropriate after graduation.

Now...

A bit early, both are still students, and her dowry hasn't been saved much yet.

Anyway, this guy can't run away.

Song Yao thought in her heart.

"Not many years left."

Xu Qingzhou wasn't that anxious either. The two now were no different from those married couples, except for the lack of a marriage certificate.

Tuesday morning at 8:00, Xu Qingzhou and Song Yao went out together, drove to MIT, and like last semester, substituted for Professor Roberts' class.

*Analytic Continuation*, a course in complex analysis. Complex analysis is generally a follow-up course to "Mathematical Analysis," a professional course for math majors.

Analytic continuation is considered more detailed.

"Good morning, Senior."

Sun Simin waved to greet him.

Sun Simin, Dino Connelly, Ma Ersi, and several others were still taking this course, considered old acquaintances.

Xu Qingzhou looked at the dazed girl and asked with a smile: "You finished the problem I left last week, right?"

"No," Sun Simin said with some shame.

"Don't be discouraged, this problem really has difficulty."

Xu Qingzhou comforted her. He also spent an afternoon solving it back then. This is a problem of the boundedness of maximal operators in harmonic analysis.

The tiered classroom was already sitting with more than forty people. Besides the 23 students taking the course, the others were all auditing. As Xu Qingzhou walked in, the classroom gradually quieted down.

"Let (t) be the Hardy-Littlewood maximal operator, defined as: 【tf(x)=\sup_{r>0}\frac... Prove the weak boundedness of the following generalized form of the operator: 【t_\alphaf(x)=\sup_{r..."

"Which of you students solved it yourself?"

No response.

Xu Qingzhou wasn't surprised, took a marker, and wrote on the whiteboard.

"Key tools: 1. Covering lemma, such as the fractal generalization of Vitali covering or Besicovitch covering; 2. Enhoupt (A_p) weight theory; 3. The singular integral operator calculation I once did on the local smoothness of Fourier integral operators."

Everything as usual, teaching class, explaining problems, answering everyone's doubts, and then discussing the fractal support of measure and Fourier transform with two scholars.

"Senior, let me treat you to a meal, just right to ask two questions."

Sun Simin waited until the end.

"Sure."

Seeing it was indeed time to eat, Xu Qingzhou nodded, packed his things, and came out with Sun Simin.

The two entered a pizza shop.

After ordering, Xu Qingzhou took a photo first to report his itinerary to Song Yao.

"Senior, you and Senior Song have such a good relationship," Sun Simin said with some envy.

"It's okay."

Just occasionally beaten.

He put down his phone and said directly: "There's still a while, let's talk about your problem first."

"Okay, okay."

Sun Simin handed over the manuscript.

Both were problems on the analytic continuation and zero distribution of Dirichlet series.

"Where did you see these two problems?"

"Saw them in Tao Zhexuan's *Analytic Theory of High-Dimensional Sieve Methods*."

"This level of difficulty is still a bit early for you, but we can talk about it. The most important thing is to analyze the relationship between analytic continuation and the asymptotic behavior of partial sums."

After eating, Xu Qingzhou didn't stay long, carrying his computer to the library.

Having rested for several days, he was prepared to try other calculations related to the Riemann Hypothesis.

Mathematical methods don't work, so introduce physical tools.

He had spent most of his energy on mathematics these two years, almost forgetting the quantum mechanics he had mastered in his previous life.

No one understands quantum mechanics better than him.

The Riemann z-function is very likely to correspond to a certain quantum mechanical energy level, and the distribution of its non-trivial zeros is the same as the eigenvalue distribution of random Hermitian matrices.

Combining the Riemann z-function and quantum mechanics is the mainstream research direction for physicists who are currently keen on using physics to solve the Riemann Hypothesis.

In Xu Qingzhou's view, this method is in a certain sense more difficult than the mathematical method, and can even be said to be ethereal.

After all, it's wanting to connect two different fields.

First, one must prove that a certain system in physics is completely consistent with the zero distribution of the Riemann Hypothesis.

However, what if one only cites certain physical tools to assist his existing calculations?

Xu Qingzhou first went to find the administrator to borrow the manuscript of mathematical physicist Berry, who had once made attempts in this regard.

Berry had done research in this area, once defining an energy level density function of a quantum system that was completely similar to the density function of the non-trivial zeros of the Riemann z-function.

Borrowing the manuscript, Xu Qingzhou found an empty seat in the library and sat down.

He also planned to start from the energy spectrum, first trying to find a way to create a useful tool—an energy level density function—with the final goal of creating a special random Hermitian matrix to make up for the deficiencies in mathematical calculation.

(End of chapter)