A Genius Mind, Demonic Logic

Shen Qi wrote his opinion on the blackboard:

Res(g(s)-2k)=Τ(s)ζ(s)(2α)^-s...

"When k is greater than or equal to 1, s=0 is a first-order pole of g(s). In the integral of this formula, I transform τ to -2k-s..." Shen Qi stated loudly, tapping an expression on the blackboard. "Then we get this expression. The sum path transformation can be reduced to the sum in the twin-matching method. Based on this setting, the first expression of ζ(s) that I obtained is valid. In other words, I did not use any theory from the Hardy system. The Hardy system is a classical system, but the 21st century needs new and more advanced systems. Thank you."

Shen Qi's eloquent and well-reasoned speech won the approval of most of the experts present.

"There are contradictions between Euclidean geometry and Lobachevsky, but both systems are being used, and there is no absolute right or wrong," Kabrovsky said, adding that he supported Shen Qi on the first question.

"We have studied Newton classical mechanics and Quantum Mechanics. Newton was not wrong, and Einstein and Schrödinger were equally correct," Rodrigues added.

"Shen is an excellent scholar, but no one can compare to Einstein, Schrödinger, Lobachevsky," Maynard said, sounding somewhat agitated.

"Don't get so excited, Professor Maynard. I think Professor Kabrovsky and Professor Rodrigues are right. Shen's twin matching method and Hardy system are not contradictory. Day and night cannot exist at the same time, but they are both meaningful." The neutral Canadian mathematician Carrick gradually leaned towards Shen Qi. He believed that Shen Qi's solution to the first question was reasonable and logically sound, and that Shen Qi's new theory was valid.

"Professor Kabrovsky, Professor Rodrigues, Professor Carrick, regarding the first question, we have been discussing it in Sweden for two months, and I still support Professor Maynard's view that only the Hardy system is the only correct way to solve the Riemann Hypothesis." Australian mathematician Wilson stepped forward, clearly standing on Maynard's side.

"Hardy and Ramanujan failed to prove the Riemann Hypothesis because they lacked time, while we have plenty of time. We should continue along the correct path that Hardy and Ramanujan followed." The curly-haired Indian mathematician, Sabhasin, was indeed in cahoots with Maynard. Maynard strongly supported the British master Hardy, and Sabhasin did not forget to bring up Hardy's best partner, the pride of India, Ramanujan.

Shen Qi coldly observed the three mathematicians from Commonwealth countries. It's normal, it's perfectly normal. No matter how reasonable my words are, there will always be someone who jumps out to criticize me.

At this moment, Nakamura Kenji, a mathematician from the University of Tokyo, stood up, walked to the blackboard, picked up the chalk, and began to write:

ρ1,1-ρ1

ρ2,1-ρ2

ρ3,1-ρ3

ρn,1-ρn

ζ(s)=e^A+Bs∏∞n=1(1-s/ρn)(1-s/1-ρn)e^(s/ρn+s/1-ρn)

After finishing writing, Nakamura Kenji said, "I studied Shen's twin matching method in great depth. Using the vertical combination method, I derived the exact same conclusion as Shen's first expression. We should respect the facts and the laws of mathematics. Shen's theory is correct; it is an indisputable and fundamental mathematical principle."

Shen Qi was quite surprised. "Wow, Nakamura, this Japanese guy, actually supports me! He used the Fundamental Theorem of Algebra to verify my twin matching method and the first expression. Quite an idea! Brilliant!"

Justice will prevail. Mathematicians with true conscience and professional ethics focus on mathematics itself, and all other factors are not within the scope of their evaluation.

Starting from the Fundamental Theorem of Algebra, Nakamura Kenji verified that Shen Qi's new theory was logically sound.

"I still stand by my point of view, and I will abide by the jury's rules. In the final decision-making process, let's vote." Maynard was particularly stubborn, just like most Britons.

The current situation is: 4 for supporters, 3 for opponents, and 4 for neutrals.

Shen Qi thought to himself, "In your voting process, to accept my proof of the Riemann Hypothesis, do I need more than 50% or more of the votes?"

Is it a veto system?

The voting rules need to be clarified, otherwise Maynard will be determined to target me relentlessly, and then what's the point of even doing it?

"Six votes. If 11 of us cast six or more votes in favor, including six, then IMU and the Journal of Mathematics will recognize your paper." The head of the review panel Kabrovsky, explained the voting rules to Shen Qi.

"It's fair, isn't it?" Shen Qi Sun Yat-sen University and asked, "So we don't need to dwell on the Hardy system anymore, right?"

"Let's move on to the next question, one that has been on my mind." This time it was Kabrovsky's turn to ask a question. He asked Shen Qi, "How do you explain that under the premise of the twin-matching method, ρ must be a first-order zero?"

That's a great question. It's professional, insightful, and high-class.

Kabrovsky's questions were objective and fair, based on mathematics itself, Shen Qi felt it was necessary to explain this clearly to the judging panel.

Shen Qi answered the questions with great enthusiasm, and it was already noon by the time he finished answering the second question.

For the entire four hours that morning, Shen Qi answered only two questions.

The review experts are all very professional; they pay attention to any questionable details, which cannot be resolved in 45 minutes.

To pass the review, the proof of the Riemann Hypothesis based on the 'twin matching method' would mean that at least six experts would have no questions about any detail. In other words, Shen Qi would need to get more than six perfect scores.

An afternoon passed, and Shen Qi perfectly answered the two new questions.

Working late into the night, until the early hours of the morning, Shen Qi was exhausted after the judging panel asked a total of eight questions that day.

Fortunately, the result was satisfactory. Shen Qi's intuition told him that the number of supporters had reached about six.

As dawn broke, the review continued. On the second day of the review, Shen Qi answered five questions.

After three days of continuous interrogation, Shen Qi pulled through, but the elderly Captain Kabrovsky collapsed from exhaustion.

On the fourth day, Kabrovsky, despite being ill, took up his post and asked the last question of the review, "If the Riemann Hypothesis holds true, then Shen, how do you explain logζ(σ+it)<<(log∣t∣)^2-2σ+ε, where ∣t∣≥2, ε>0, 1/2≤σ≤1?"

According to Shen Qi's observation, the current situation is 6 for supporters, 3 for opponents, and 2 for neutrals.

With the last question answered, the outcome is decided!

This problem is a new one derived from the main body of the paper. Shen Qi picked up the chalk and wrote on the blackboard. After writing a set of equations, he tapped the blackboard and said excitedly, "I have proven that on the circle |s-s0|≤3/2-σ, logζ<<σ^-1log|t|, |t|≥2. Obviously, the constant << here is independent of σ! Independent of σ!"

Shen Qi erupted with tremendous force!

Maynard was startled and accidentally spilled coffee on his trousers.

Apart from Maynard, Wilson, and Sabhasin, three Commonwealth mathematicians who were seated, the other eight mathematicians stood up, their expressions excited.

"Shen, you actually came up with this proof method in such a short time!"

"A perfect proof! The Riemann Hypothesis is a correct proposition!"

"Let's vote! Yes, there's nothing more to ask. Shen is a genius, let's vote for a genius!"

Knock knock!

Shen Qi tapped the blackboard. "Please sit down, everyone. I haven't finished speaking yet."

The situation was excellent, and the eight mathematicians on the judging panel were completely won over by Shen Qi.

There are now 8 votes in favor!

Shen Qi has practically become a god; it's only a matter of time before he becomes one.

A mix of emotions filled the meeting room: admiration, applause, frustration, helplessness, and resignation.

Under everyone's watchful eyes, Shen Qi suddenly had an inspiration and wrote down a new formula. He excitedly pounded the blackboard. "If the Riemann Hypothesis holds true, there is another case where, when 1/2 + (loglog∣t∣)^-1 ≤ σ ≤ 1, we have logζ(s) << (loglog∣t∣)(log∣t∣)^2 - 2σ, where the constant << is an absolute constant! An absolute constant! Perfect, it's perfect!"

Brush!

Indian mathematician Sabhasin jumped up involuntarily, his eyes the Boss, his curly hair standing on end. "Yes, he's right! Genius imagination, devilish logical deduction..."

Seeing Sabhasin's possessed appearance, Maynard was furious. That Indian was so unreliable; had he been turned by Shen Qi?

Maynard looked at the blackboard. As Series Theory expert, he had to admit that Shen Qi truly possessed a genius-level brain and devilish logic...