The Complete Package

"The proof of the Riemann Hypothesis involves two core expressions, which I reported on in March of this year. In this report, let's briefly review the proof of the Riemann Hypothesis."

Shen Qi spent a few minutes briefly reviewing the important process and main conclusions of the proof of the Riemann Hypothesis.

"... That concludes the overview of the Riemann Hypothesis. Now, we can directly apply Riemann Theorem."

Regarding the Riemann Hypothesis, a research finding from more than half a year ago, Shen Qi explained it very simply, quickly going over it in a flash.

One cannot live in the past, in memories.

For Shen Qi, the Riemann Hypothesis is a thing of the past; a grander goal awaits him to conquer.

But the audience in the lecture hall knew that Shen Qi's simple explanation did not mean that the Riemann Hypothesis was simple.

No matter how brilliant Schultz was, he ultimately did not completely prove the Hodge conjecture.

Perelman proved the Poincaré conjecture; however, this eccentric Russian did not attend the 2006 International Congress of Mathematicians and the Fields Medal award ceremony.

So far, only two mathematicians have solved the Millennium Prize Problem. Shen Qi stood before mathematicians from all over the world to present his research results.

"Based on the proof of the Riemann Hypothesis and the first two expressions, Shen Qi should be qualified," Gong Changwei said softly.

"That makes sense, it just depends on how IMU decides," Yun Wei nodded and said.

"If Shen Qi succeeds in increasing the stakes, the RT Third Expression will be completely completed, which will make things even safer," Xu Yang said.

On stage, Shen Qi began his report on "Riemann Theorem and its Supplementary Theorems," which was the focus of his presentation.

"More than two months ago, at the Ramanujan Prize conference in Italy, I presented the framework of RT Third Expression. Twenty days ago, I published the specific technical details based on that framework on arVix."

"The derivation of the RT Third Expression will prove a supplementary theorem to Riemann Theorem."

"So, did I actually obtain the RT Third Expression?"

Shen Qi looked down at the audience and calmly answered his own question, "The answer is, it has been thoroughly verified, just a few days before I came to Brazil."

Brush!

Swish!

Someone in the audience stood up.

All eyes were on Shen Qi and the big screen.

Favorite candidates such as Faltings, Blund, Ayoub, and Schultz are paying close attention to Shen Qi. They have studied Shen Qi 'Shen Qi previous reports and are eagerly awaiting his latest report.

If Shen Qi's performance is successful, one of the four European mathematicians may miss out on this year's Fields Medal.

The four European mathematicians were all experts; they understood the significance of the Riemann Hypothesis and the landmark mathematical value of the supplementary theorems to the Riemann Theorem.

Riemann Hypothesis + Riemann Theorem + Supplementary Theorem: If Shen Qi completes the entire research process from start to finish...

Schultz was a little nervous, and so was Faltings.

Blund and Ayoub remained as steady as ever, watching Shen Qi with admiration and anticipation.

"The first path, through the function logζ(s), we obtained that ∏L(s,Χ) is analytic at the point s=1 and is also equal to zero. This corollary is very meaningful, and I would like to thank my academic partner, Mr. Jonas -Carl."

"The second approach, based on the fundamental theorem of prime numbers, proves that when c is a positive constant dependent on A and A > 1, π(x; q, l) = Lix/φ(q) + O(xe^-clogx). I would like to thank my academic partner, Ms. Mary -Schmidt."

Shen Qi looked down at the audience, at the seats where his team was located.

Mary and Jonas smiled, feeling proud to be part of this great cause.

Schultz, standing a considerable distance away, wore a complex and peculiar expression.

"Mary, you..." Schultz's gaze shifted to the audience, searching for his wife in the crowd.

Schultz already knew that Mary was helping Shen Qi with his work.

Mary's name was among the four authors of the paper Shen Qi previously published.

Even though he was mentally prepared, Schultz still felt uncomfortable.

After all, in front of mathematicians worldwide, it was not Schultz, the legal husband, who thanked his wife, but Shen Qi.

On stage, Shen Qi continued switching PPT slides, "The third path, when T is not the ordinate of the zero of L(s,Χ), we obtained an important equation for the zero-point property of the Zeta function, and successfully rewrote it into a system of ordinary equations, namely the system of equations on the big screen: x=βk, γ=γk, x^2-x-γ^2+γk^2+βk-βk^2=0, γk(1-2β)+γ(2x-1)=0. I would like to thank my girlfriend Ou Ye."

Ou Ye welled up with tears, and the audience below buzzed with discussion.

"Girlfriend? What a romantic combination."

"The last person Shen Qi thanked was Mary Schmidt; her previous name was Mary Schultz -Schmidt."

"Peter Schultz's wife?"

"Perhaps she's now called his ex-wife?"

"Peter Schultz's wife, or ex-wife, helped Shen Qi conquer RH and RT; Shen Qi should be awarded."

The mathematicians shared their views, and the hall suddenly erupted in noise.

"Thank you, thank you everyone for your attention." Shen Qi took control of the situation and continued, "The content up to this point is not much different from what I announced 20 days ago. I've made some optimizations to make the conclusions from the three paths more concise."

"I know everyone is concerned about the four paths, and now I will announce them."

"Based on the inferences derived from the previous paths, and the system of equations relating the zero-point properties of the Zeta function, we have derived a core expression, please see the screen."

The formula on the screen is:

ζ(s)=∑(0≤n≤T*-a)(n+a)^-1/2-it+O((T*)^1/2(1+t)^-1),0≤t≤T

More than half of the audience in the lecture hall stood up. It was the first time they had seen this formula, and their mathematicians' intuition told them that it was unusual.

"According to Shen's twin matching method, we can clearly know that at the zero point, this expression is obtained entirely through the transformation of the integer function ξ(s), and it is still an integer function in form."

Shen Qi spread his arms and embraced the world. "In other words, during the process of traversing the complex plane, s happens to be exactly at a certain non-obvious zero point, that is, it coincides with that non-obvious zero point. The RT Third Expression is proved! The supplementary theorem of Riemann Theorem is true!"

Shen Qi spent more than half a year laying the groundwork for the third expression of RT.

In March, Shen Qi introduced the concept of the RT Third Expression. In early August, Shen Qi published a framework report in Italy. Twenty days ago, Shen Qi announced three paths.

At this moment, Shen Qi completed his final strike, and the fourth path in his 8-page PPT finally yielded the third expression.

Oh!

The mathematicians in the audience were thrilled. Shen Qi had completed the entire research project, including the Riemann Hypothesis, Riemann Theorem, and Supplementary Theorems!