Chapter 158 - 155: How About Bringing Old Yang Along?
Li Dong froze on the spot.
’Riemann?’
Since joining the "Cyan Dragon Study Group," Riemann had only spoken once, and that was to thank him.
After that, he hadn’t said another word.
From what Li Dong understood,
although Riemann had an introverted personality, he was by no means a man of few words. He was famous for being an engrossed and eloquent lecturer in his classes at the University of Göttingen.
In other words, the silence of this Riemann from a parallel universe wasn’t due to his personality.
It was more like...
he was conserving something.
’Stamina? Energy?’
These thoughts flashed through Li Dong’s mind. He refocused and replied.
[University Researcher]: Hello, Mr. Riemann. Is there something I can help you with?
After he sent the message, the group fell silent again...
Li Dong waited for a full three minutes.
Just as he thought the other person wouldn’t reply and was about to lock his screen to take a shower,
[Bernhard Riemann]: Did you figure it out? Can you show me?
Li Dong shot bolt upright.
"???"
’No way, does this guy have some kind of divine insight?’
’That "Did you figure it out?" is incredibly specific.’
It could only be referring to the non-trivial zeros on the order of 10^23.
"Wait..."
Li Dong slapped his forehead.
’Am I an idiot?’
The dimensionality reduction algorithm he’d created came from his insights into Riemann’s Manuscript!
Whether it was the zero data on the order of 10^23 or the rigorous proof of Montgomery’s Conjecture on Association within the interval |α|∈[0, 4] derived from those zeros—
to put it bluntly, they were all fruits grown from Riemann’s legacy.
And he’d actually forgotten to share his results with Riemann?
’No wonder I can’t leech off people as well as Newton...’
Li Dong wanted to slap himself a couple of times.
He immediately replied.
[University Researcher]: Sir, I’ve figured it out. Give me a moment, I’ll organize it.
Riemann didn’t reply.
Li Dong opened his laptop.
He first bundled the complete dataset of non-trivial zeros on the order of 10^23 and his paper on Montgomery’s Conjecture into a single compressed file.
Then, he clicked send.
[Send Failed]
"Huh?"
Li Dong was stunned.
’It can’t be sent?’
He tried again.
[Alert: File content exceeds the Group Leader’s current cognitive boundary. Cross-dimensional compilation cannot be completed.]
Li Dong was completely dumbfounded.
He had run the zero data himself.
He had derived the proof for Montgomery’s Conjecture himself, too.
And now it still couldn’t be sent?
There was still something in Riemann’s Manuscript that he hadn’t fully grasped!
A wave of shock washed over Li Dong.
He had read that manuscript over a hundred times! From the saddle-point method for contour integration to the original derivation logic of the Riemann-Siegel formula, he believed he had thoroughly digested every single line of deduction.
But the group’s rules wouldn’t lie.
If it couldn’t be sent, it couldn’t be sent.
’There’s... still some real hidden depth in that manuscript?’
Li Dong took a deep breath, his thoughts consumed by Riemann’s Manuscript, and suppressed the shock he felt.
In any case, Riemann was waiting for his reply.
Whether it was for the sake of leeching or out of genuine respect for this founder of modern mathematics,
he had to get these results into his hands.
’I was hoping to do research with the big shots. Guess that’ll have to wait...’
Li Dong grumbled to himself, then tapped on [Group Functions] in the upper-right corner of the chat interface.
[Data Transfer]
Remaining Uses: 1
’Screw it, I’m using it!’
He opened the data transfer interface, selected [Bernhard Riemann] from the recipient list, and sent the compressed file.
[Transfer Complete.]
[Data Transfer Remaining Uses: 0]
Li Dong looked at the number that had returned to zero. He felt a pang of regret, but more than that, he felt anticipation.
He had no idea how Riemann would judge his achievements.
Compared to leeching, this was what he actually cared about more.
After all, having Riemann personally critique your paper—
mathematicians all over the world would kneel to listen.
Li Dong stared nervously at his phone screen.
A minute passed.
Two minutes.
[Bernhard Riemann has sent a private red packet.]
Li Dong was completely dumbfounded again.
"Two minutes?"
’Dude, you finished it in two minutes?’
He might be grumbling, but his hands moved fast.
[You have received Bernhard Riemann’s thanks.]
[Reward Obtained: All core Basic Attributes +0.1 (Permanent)]
[Description: When prime numbers twinkled chaotically in the infinite night, he alone saw the critical line that pierced the chaos.]
[With a pen and a stack of drafts, amidst the sound of coughing up blood from tuberculosis, he pursued the musical score God wrote for the distribution of primes.]
[He did not live to see the dawn, but the line he left behind became the foundation for all future edifices of number theory.]
[And now—you have seen the dawn in his stead.]
[You helped him verify that on that critical line, the positions of the first 10^23 "notes" had not deviated in the slightest.]
[From this day forth, you and that mathematical prophet share the same starry sky of prime numbers.]
The moment Li Dong tapped open the red packet, he felt something in his brain unlock with a "POP."
All his core Basic Attributes rose from 0.3 to 0.4!
This meant... his current base stats were now two-fifths of Newton’s!
[Isaac Newton]: ...
The most direct change Li Dong felt was...
he could recall the data of the non-trivial zeros.
14.134725...
21.022039...
25.010857...
30.424876...
Before, he had relied on Newton’s +1 Concentration trial card to brute-force memorize the patterns in the spacing of zeros hidden deep within the 10^19 range.
But brute-force memorization and understanding were two different things.
Back then, it was like he was looking through a layer of frosted glass, unable to see clearly.
But now...
the frosted glass had shattered.
Li Dong soon collected his thoughts and frowned.
Although this increase in Basic Attributes was great, still...
why wasn’t there a passive aura for mathematics?
He now had passive auras for physics, chemistry, biology, and even computer programming.
Only mathematics was missing one.
’I don’t know if it’s my bad luck or if mathematics as a discipline is just special...’
Just as he was lamenting this,
his phone vibrated again.
[Bernhard Riemann]: Pair correlation of zeros.
Just four words.
It was as if he were conserving every last shred of energy in his body.
About half a minute later, a second message appeared.
[Bernhard Riemann]: Their statistical properties... have some sort of necessary, equivalent connection to the local structure of automorphic functions.
Li Dong stared at the sentence and immediately began to think.
’The pair correlation properties of the zeros... and automorphic functions?’
What Riemann meant was:
The distribution pattern of the spacing between the non-trivial zeros of the Zeta function wasn’t just a statistical coincidence, but was fundamentally related to certain underlying mathematical structures of automorphic representations?
[Bernhard Riemann]: If... this connection could be rigorously proven.
After that sentence appeared, Riemann sent no more messages.
But these three sentences made Li Dong think of something else.
His 0.4 Logic attribute was firing on all cylinders.
"Pair correlation of zeros... automorphic functions... equivalent connection..."
"If what Riemann said is true, that means—I can use the pair correlation data from these 10^23 zeros to reverse-engineer and verify the properties of automorphic representations?"
Jiang Yubai: A sneak attack????
As soon as this idea emerged, it was as if Li Dong had an epiphany.
"Automorphic representations... the local-global compatibility of automorphic representations!"
He suddenly recalled a paper.
The paper had been published in the Duke Mathematical Journal.
Its title was: "On the Local-Global Compatibility for GL₂ Automorphic Representations of the Case Where the Ramification Index Does Not Exceed 2."
And the authors were listed as: Jiang Yubai¹ and Zhou Shenzhi².
Kyoto Normal University School of Mathematical Sciences.
"GL₂... ramification index not exceeding 2..."
Li Dong began to pace back and forth in his room.
"If the equivalent connection Riemann mentioned really holds true, could I then use the pair correlation properties of the zeros to generalize this GL₂ result... to GL(n)?"
From GL₂ to GL(n).
Generalizing from a special case to the general case.
Li Dong knew very well what this meant in the world of mathematics.
"If I can pull this off..."
"And then bring Old Yang in on it?"