Top Student at Their Peak-Chapter 231 - 108: The Future Qiao Yu-Qiao Xi’s Upper Bound Theorem!_5

Schulz’s five papers on the theory of quasi-complete spaces, he had already read them all and digested most of it, and during this time, he also supplemented a lot of fundamental knowledge. He basically completed the proof of his wild proposition.

According to his original idea, let X be a high-dimensional algebraic curve defined over a number field K, and X is a closed subset of a p-adic complete algebraic space. Then there exists a constant C that depends on the geometric properties of the curve X, such that the number of rational points on the curve satisfies: N(X)≤C.

This constant C does indeed exist, and Qiao Yu even feels that his proof process is already quite perfect.

Moreover, he has also derived the formula for this constant C.

In other words, on the night he arrived at Yanbei University, his imaginative proposition really had been proven by him.

If it weren’t for that Professor Zhang, he might have already enthusiastically started writing a paper to announce his discovery to the mathematical community!

But he hasn’t started writing yet because the formula for this constant C turned out like this:

Finally, after solving for C1, C2, C3, the specific expression looks like this:

Three constants A1, A2, A3 were introduced, representing constants related to Modular Forms, -adic homology, and categorization of quantized homology respectively. And α, β represent exponents related to these geometric constraints, of course, the deficiency g is still the main factor determining the upper bound.

Useless, totally useless.

Qiao Yu tried to integrate it into Professor Robert’s work, hoping to use his formula to solve some application problems, and then quickly found that determining the level k of Modular Forms, the choice of a prime P, and the determination of the quantized homology parameter C, were all too complex.

The constants A1, A2, A3 in the formula, as well as constants α, β related to determining geometric structures all depend on specific geometric backgrounds and curve types, and when Qiao Yu actually started to calculate by hand, he discovered how troublesome it was.

During this time, he has been thinking about how to simplify the formula, so that it can be made usable, and still hold true, he thought of many ways, but encountered obstacles everywhere.

He can somewhat understand the feeling of Senior Brother Chen of facing research headaches, every time he thinks of a possible solution to this problem and rushes to the computer excitedly to start solving it, reality always gives him a blow.

Every attempt ends with a dead end.

He even asked Old Xue specially, and Old Xue’s suggestion was not to hope for finding a universal formula, but to directly simplify for specific situations, reducing complexity in particular problems.

This way, there could still be a certain practical application space, and it wouldn’t be completely without value. freёweɓnovel.com

For example, making a simplified formula specifically for a certain type of simple elliptic curve.

This is certainly a way, and Qiao Yu could even use this method to draft several thesis, like one for elliptic curves, one for parabolic curves, one for hyperbolic curves... and for more sophistication, he could project curves of algebraic varieties and high-deficiency hyperelliptic curves...

But Qiao Yu feels this has no meaning, after all, his original intention was to create a universal formula, directly published in the top four journals, later named by the world mathematics community as "Qiao Yu Upper Bound Theorem" kind of paper!

Qiao Yu feels that if it doesn’t reach this level, he can’t add glory to the teachers and grandmaster.

Moreover, with his current status, if he chooses to draft a thesis, it not only holds no meaning for him, but also may invite much criticism, making Director Tian’s face look bad, he might as well study quietly.

After all, he doesn’t plan to hold a position at some university and need to publish papers for academic titles or anything like that.

He just mentioned in the group about getting results before the IMO competition, which can be considered as setting a time limit for himself...

Of course, if Tian Yan Zhen and Yuan Zhengxin knew Qiao Ze’s thoughts, both of them would probably curse him out, hoping they could wake up this kid, and stop thinking about all sorts of nonsense, wasting time!

After all, wanting to eponym a theorem at fifteen is somewhat too naïve. Although if Qiao Yu really solved this problem, it indeed does have that possibility.

But where is a simple, universal upper bound accurate estimation formula so easy?

Professor Robert Green has researched this direction for so many years, and has only been looking for relatively accurate results in various special curves.

But Qiao Yu’s idea is obviously a bit different.

Back then, Euler at the age of sixteen was able to graduate with a master’s degree, proposed to compare Cartesian and Newtonian philosophical systems, and Gauss at fifteen independently discovered the root-finding method for cubic equations, why can’t he, Qiao Yu, propose an Upper Bound Theorem at sixteen?

Thus naturally, Qiao Yu stubbornly tackled this topic head-on, it’s just quite frustrating now! It hit hard, these two good friends couldn’t compensate for this kind of frustration...

...

At the same time, in a key middle school in Shuangqing, a little fat kid, with a crying face, looked up holding a phone and said to the teacher next to him: "Teacher Qu, Qiao Yu suddenly doesn’t play fair! He agreed to pay fifty bucks per question, but now he won’t talk to me."

The teacher sighed and said: "Oh, if you don’t understand, you don’t, why are you so anxious? Let me research for two more days."

...

In a self-study room equipped with computers and the internet at Linhai International School, Yu Wei quit the group chat with a livid face. He was indeed furious, as when he was reminded by that darned fatty about the ambiguity of his words, it was already impossible to take back...