Chapter 430: The Riemann Hypothesis

During the New Year period, Xu Qingzhou wasn't busy with those complex calculations. When he was free, he accompanied Old Xu and Ms. Wang to watch TV, or just read materials at home.

What he was reading now was the content of the Euler-Maclaurin formula, which is a formula for calculating zeros.

The problem of the Riemann Hypothesis was still stuck at where it was before the New Year.

Just as mentioned before, Xu Qingzhou divided the proof of the Riemann Hypothesis into three steps, so now it could be completely considered as being on the road to climbing the main peak.

He was still doing calculations to hunt for zeros.

As t increases, because the negative power of t in the higher-order terms is relatively high, its contribution becomes smaller and smaller. To strictly express this trend and prove it, one needs to analyze its convergence and error estimation.

After this, he still needed to use the rough estimates of Dirichlet polynomials that Professor Maynard and the others had researched a few days ago, and make modifications so that he could complete the upper bound estimation of the distribution of non-trivial zeros of the Riemann z-function.

In short, it was very complex, giving a feeling of being difficult to overcome.

This could be considered the first vertical glacier encountered while climbing the main peak.

For this reason, Xu Qingzhou planned to spend a month to settle the estimation of the upper bound problem of zero distribution.

Bedroom, Xu Qingzhou was calculating at his desk.

"Fruit."

Wang Xiaping brought in the cut apples, glanced at the first manuscript on the table, and revealed the "subway old man" meme expression.

The whole page was full of strange symbols, without a single word of explanation.

"Mom, watch out for my manuscript." Seeing there were still water stains under the plate, Xu Qingzhou hurriedly moved the manuscript on the table so Wang Xiaping could place the plate.

Wang Xiaping looked at her son's cautious appearance. "Aren't they just a few sheets of paper? Making them look like some kind of treasure."

"These things are much more precious than treasure."

Xu Qingzhou stuffed a piece of apple into his mouth and laughed: "In the future, these things might be able to be stored in a library."

Wang Xiaping was greatly surprised. "Can a few sheets of paper be put in a library?"

"Of course, things about scholars are just that magical. In the future, the house we live in could become a cultural relic," Xu Qingzhou said boastfully.

"Stop talking nonsense, hurry up and ask when Xiao Yao is coming over."

Wang Xiaping felt more and more that this brat was talking nonsense, but she thought of the serious matter for the evening.

"Mom, it's only 2:30 in the afternoon."

"It's already 2:30? Hurry up and ask; I have to go buy groceries. Xiao Yao said last time she wanted to learn how to cook that dish from me..."

After urging Xu Qingzhou, Wang Xiaping seized the time to go buy groceries.

Bang~

The sound of the door closing came from the living room.

Xu Qingzhou shook his head, messaged Song Yao to ask when she would arrive, and scanned the thick manuscript paper on the table.

The manuscript he brought back this time was about two hundred pages.

He actually wasn't bragging; the manuscript was indeed very precious. Of course, if he could prove the Riemann Hypothesis, these manuscripts would be priceless treasures.

Just like the manuscript Riemann left in the library of the University of Göttingen, after Riemann passed away, countless mathematicians and historians went to study it.

However, it could only be said that they went full of hope and returned empty-handed.

Because the content of the manuscript was whimsical, with countless topics intertwined together.

This was also normal. Even for the things in Xu Qingzhou's hands, if he didn't explain them personally or add some notes, it was estimated that not many people could understand the logic.

Ever since the Riemann Hypothesis came out, mathematicians had followed one after another, hoping to crack the mystery.

In the 44th year after Riemann's paper was published, mathematician Gram calculated the first 15 non-trivial zeros of the Riemann z-function using the Euler-Maclaurin formula.

Then, until 1925, after the efforts of Hardy, Littlewood, and others, they only calculated 138 zeros.

It wasn't until 1932 that mathematician Siegel finally found clues in Riemann's heavenly book-like manuscript—a calculation method for the non-trivial zeros of the Riemann function.

This was the Riemann-Siegel formula that Xu Qingzhou was still improving earlier.

At this stage, computers had verified that more than 1.5 billion non-trivial zeros satisfied the property of real part 1/2, but it was still impossible to exhaust all situations. Although the data results supported the hypothesis, this could not replace a mathematical proof.

It's hard.

"Phew~"

Xu Qingzhou rubbed his temples, put down the manuscript, and the phone screen on the table lit up. Song Yao sent a message.

4:00 PM.

Dong~ Dong~

The sound of knocking on the door pulled Xu Qingzhou back from his calculations.

Open the door.

"How are you two together?"

He looked at the two women carrying groceries at the door and was stunned for a moment.

"Met on the road. Look at you, all you know is staying at home all day, unshaven."

Wang Xiaping originally didn't feel anything, but compared to Song Yao, she suddenly felt that her son and Song Yao were completely on two different layers.

College entrance exams, awards, and such didn't count for much; that her brat could find a girlfriend like Xiao Yao might really be the ancestral grave smoking.

Wang Xiaping sighed in her heart.

Song Yao was used to it. After this guy stayed at home for several days, he was even sloppier than now.

"Why shave at home."

Xu Qingzhou muttered in a low voice and closed the door.

On this side, Wang Xiaping and Song Yao carried the groceries into the kitchen.

"No need, no need, Xiao Yao, you sit with Qingzhou first. I'll teach you that dish in a while."

Wang Xiaping pushed Song Yao out. This girl was dressed so well, and she was so tender she could be pinched to produce water; staying in the kitchen would easily get her covered in oily smoke. She would let her in when it was time to learn the dish.

"Sit down first." Xu Qingzhou pulled Song Yao to sit down.

Song Yao looked around and asked: "Where is Uncle Xu?"

"Went to find a friend to play chess."

Xu Qingzhou leaned toward Song Yao. Not having seen her for a few days, he wanted to kiss Song Yao on the face.

Song Yao pushed him away and kept a safe distance. This was in Xu Qingzhou's house; what would it look like to be handsy? What if Aunt Wang saw...

"Do you dislike me?" Xu Qingzhou was resentful.

"Mm."

Song Yao nodded.

"..."

"Alright, actually I have big news."

Xu Qingzhou lowered his voice and said mysteriously.

"What big news?"

Song Yao wrinkled her nose, half-believing, always feeling that this guy definitely had nothing good.

Xu Qingzhou leaned closer.

Song Yao didn't dodge this time, pricking up her ears, wanting to hear what big news Xu Qingzhou had, and then heard this person say quietly: "Let's go to the bedroom; I'll show you a video of Er Miao doing a backflip."

Bang~

Wang Xiaping came out of the kitchen with a spatula, her expression strange: "Did you two hear any sound?"

"No."

Song Yao sat upright, turned her head to look at Xu Qingzhou: "Did you hear it?"

"No."

Xu Qingzhou shook his head dishonestly.

"Looks like I'm getting old..." Wang Xiaping shook her head with a smile. "Qingzhou, call your dad and tell him to come back for dinner; all he knows is being outside all day."

"Auntie, I'll help you."

"You... alright, come, put on the apron, don't get your clothes dirty."

Only Xu Qingzhou was left in the living room.

"Hiss~ Where did this girl get such strength..."

(End of chapter)