Chapter 442: Will See a Miracle

Xu Qingzhou seemed to have been hit by a bullet; his voice stopped abruptly.

The lecture hall was also silent; everyone held their breath, staring at the young man on the podium, their eyes showing astonishment.

"What happened?"

Everyone was puzzled, but no one made a sound to disturb him, quietly waiting for what would follow.

Xu Qingzhou stared at the equation on the whiteboard, his brows furrowed, reflecting on the sentence just now. "Introduce an interaction term... Introduce an interaction term... Besides here, can it also work on the density function that follows?"

Xu Qingzhou's throat felt a bit dry.

It seemed he had found the point he had overlooked!

All along, he had focused on using physical tools to compensate for the disadvantages of pure mathematical calculation, forgetting that he could use the properties of the Riemann zeta function to perform reverse calculations on the density function.

The density function sp might just be able to satisfy the calculation of non-trivial zeros.

"Hoo~"

Xu Qingzhou suppressed his excitement; this feeling of sudden inspiration was fascinating.

Like an explorer falling into a Klein bottle, inspiration was a beam of light shining through the bottle's mouth. Because of it, one could move forward along the footprints extending infinitely along the Möbius strip—the starting point and the end point quietly closing on the Riemann surface.

At this moment, all previous confusion seemed to clear up instantly.

He picked up the water-based pen again, and the sound of rustling writing echoed in the lecture hall once more.

A row of complex formulas appeared on the blackboard.

Introduce an interaction term... Then use the properties of the Riemann zeta function to deduce backwards.

Two minutes passed.

"It can work!"

Xu Qingzhou's eyes lit up. Without wasting time, he pulled down a clean whiteboard and wrote rapidly.

However, it was completely different from the previous equation; there were no physical formulas, but purely mathematical formulas for calculating non-trivial zeros.

Bakesi Kaisen, who was at the very front, saw something. "Is he trying to..."

"What... is this?"

Ma Ersi's face showed confusion. He could only recognize some Riemann function markers, but when they were all put together, he didn't recognize them.

Sun Simin and the others shook their heads; they didn't understand it either.

It was a middle-aged man behind them who said in a deep voice: "If I'm not mistaken, this is the proof of the Riemann Hypothesis that he hasn't announced yet. My God, I have never seen such a complex yet perfect formula."

That's right, Xu Qingzhou was modifying the previous proof of the non-trivial zero estimation so that it could be coupled with the density function from just now.

Mathematical calculation often involves the whole body with one pull.

He started recalculating almost from the first third of the beginning, that is, from the ξ(z) function he had constructed.

"Is he trying to prove the Riemann Hypothesis on the spot?"

"It should be. Maybe he just had some new ideas."

"Yesterday I saw a few idiots commenting that he was writing blank checks to the mathematical community. It made me so angry I wanted to stuff the terrible sandwiches from that broken shop outside the school into their mouths."

There was whispering in the audience, and even a commotion. Everyone's spirits were lifted. What a great feat it was to prove the Riemann Hypothesis on the spot.

"Boles, what are you doing?"

"Call Laike over. This is a time to witness a miracle. Compared to a date, I think he would prefer this!"

Xu Qingzhou was completely immersed in the world of mathematical operators. Analytic continuation, zero encirclement, integral representation, Hermitian operators—various tools blended together.

He didn't notice that at the left door of the lecture hall, a bearded middle-aged man was staring blankly at the whiteboard.

"I'm fucking awesome."

Horn couldn't help but swear. He had just finished delivering materials to a professor in the building next door and originally wanted to come over to go to the office with Xu Qingzhou. Who could have imagined he would see such an explosive scene.

After sighing, he came back to his senses and took out his phone: "Professor, Xu Qingzhou seems to be proving the Riemann Hypothesis in the lecture hall."

There was silence on the other end of the phone, followed by the sound of a door slamming: "Coming right away!"

At this time, the whiteboard in the classroom was no longer enough. Bakesi Kaisen, having a good eye, took an eraser and wiped away the extra physical formulas Xu Qingzhou had written earlier.

"Thank you."

Xu Qingzhou thanked him simply and returned to his previous state.

In the lecture hall, a group of people stared at the equations constantly appearing on the whiteboard, their eyes astonished. Of course, since most of the people in the class were students like Sun Simin, their knowledge base was limited, and they certainly couldn't understand it.

But this didn't affect their excitement, and because Xu Qingzhou was substituting for the class, they felt a strong sense of participation.

The other group consisted of the scholars and professors at the back of the classroom.

Some were holding pens and calculating along, some were lost in thought, and others were exclaiming repeatedly.

When Professor Roberts arrived, he looked at the lively classroom and was stunned for a moment. He first looked at Xu Qingzhou writing on the podium and took a deep breath to calm his breathing.

At the back of the lecture hall, he saw several old acquaintances and immediately walked over.

"Hi, Roberts." The old man greeted in a low voice.

Professor Roberts lowered his voice and said with some emotion: "I didn't expect you to have received the news too."

"I originally planned to go to lunch, but I heard from students that a miracle was being created here." The old man said with a smile, but his verification on hand didn't stop. He muttered: "Strange, how did he convert the integral interval of the main term of equation (17) to here..."

The old man shook his head, no longer dwelling on it, his gaze falling on Xu Qingzhou: "Do you think he can succeed?"

"It's hard to say. He is very young, energetic, and full of wisdom, but this is the Riemann Hypothesis."

Professor Roberts paused.

Youth is capital. Unlike old guys like them who could only do research by the book, he believed that Xu Qingzhou would solve this problem one day, but he had never thought this day would come so quickly.

On the podium, Xu Qingzhou was still brainstorming, using equations one by one to peel the cocoon and find the true meaning of the Riemann Hypothesis.

Ma Ersi nudged Dino Connally next to him with his elbow, signaling him to look behind.

Dino Connally turned his head and indeed saw several white-haired old professors behind the lecture hall.

Various correlation functions of the eigenvalues of random Hermitian matrices can be calculated through the integral of the distribution density to compensate for the deficiencies of pure mathematical calculation.

This requires the ξ(z) function created earlier.

The whiteboard in the lecture hall was soon full, but Horn had been prepared long ago, bringing several people to borrow five whiteboards from the nearest office.

"ξ(z) function? Amazing, it's written too perfectly."

"The density function can actually be like this!"

"My God, I have a premonition that I will definitely see a miracle today!"

One hour passed.

The number of people in the lecture hall increased rather than decreased.

Many were scholars who had heard the news and came over. Even people from Harvard and Boston University had rushed over; the Boston mathematical circle was only so big.

And those students who were originally attending the class didn't leave either.

Young people like to join in the fun, especially admiring Xu Qingzhou's personality-filled behavior.

Xu Qingzhou was completely unaffected, in a state of epiphany, with only infinite equations in his mind.

One o'clock in the afternoon.

For any o > 1/2, (n(\sigma, t) \ll t^{\epsilon})

That is: n(o, t) = 0

Thus, it is proven that all non-trivial zeros of the Riemann zeta function lie on the line re(s) = 1/2 in the complex plane.

Xu Qingzhou grinned. This tough nut to crack had finally been cracked by him.

He turned his head and only then noticed that the lecture hall was full of people.

(End of chapter) ===== CHAPTER 443 =====