The top student must be diligent

Finally, he smiled and said, "I think it won't be long before we can go to the celebration banquet."

Xiao Yi also smiled and nodded, "That's true."

"But what I didn't expect was that there was such interaction between the Circle Method and Xiao's Development. Perhaps, there are more possibilities between them..."

Turning his eyes back to the blackboard, a faint light flashed in his eyes, and he was thinking again.

Zhang Yitang stopped talking and didn't bother Xiao Yi again.

At this time, he had deeply realized that he should never influence Xiao Yi when he was thinking.

Recalling the time when he talked to Xiao Yi just now, it must be when the latter was thinking about the key. If his words influenced others, he probably wouldn't be as excited as he is now.

As for what Xiao Yi said, there are more possibilities of combining Xiao's development with the Circle Method...

He also raised his head and took a look at the previous argumentation process of Xiao Yi.

It seems that there are indeed quite a lot of processes that can be explored.

The only problem is that he can't think of which angle to start digging from for the time being.

Forget it, let's not think about it anymore, anyway, he just wants to solve the Landau-Siegel zero-point conjecture now.

However, Xiao Yi did not think for too long. He soon shook his head and turned to Zhang Yitang and said, "Okay, Professor Zhang, do you have anything else to study?"

"Me? I don't have any." Zhang Yitang waved his hands repeatedly: "The biggest problem has been solved, and the remaining small problems... won't take too much effort."

"That's true." Xiao Yi smiled and said, "Then let's stop here today. You must be tired after driving all day. You should rest early. In the remaining few days, try to solve the last few small problems. Maybe we can get the paper out before returning home."

Zhang Yitang laughed: "That's right!"

Then he patted Xiao Yi's arm, "It's my blessing to have you."

Xiao Yi waved his hands modestly: "It's mainly because Professor Zhang has made enough achievements before, otherwise it wouldn't be solved so quickly."

"Okay, there's nothing to say about this matter."

Zhang Yitang didn't argue too much about this matter.

Anyway, he knew very well that Xiao Yi's achievements saved him many years of time.

...

After leaving Zhang Yitang's office, they returned to their respective residences.

Back in the dormitory where he was staying temporarily, Xiao Yi couldn't help but sighed as he looked at the environment that was completely different from the previous dormitory.

Is this also a life of traveling?

It's just that he doesn't have to spend any money at all.

By the way, he also made a lot of money...

Sitting in front of the desk, he took out the draft paper and continued to write about the circle method on it.

For him, today's learning task has not been completed yet, and the remaining time needs to be used for research.

He wants to further explore the relationship between the circle method and Xiao's expansion.

Maybe he can discover a newer technology.

In addition...

"The circle method is the key method to solve the Goldbach conjecture."

"If it can be used..."

His eyebrows were slightly raised.

After solving the twin prime conjecture, what should be the next mathematical goal?

He thought about a lot, such as the n^2+1 prime conjecture that is already under research, or another Legendre conjecture.

These two problems, like the twin prime conjecture, are all prime number problems, but now, because of his thinking about the circle method, his attention has gradually turned to the Goldbach conjecture.

In the past, many breakthroughs related to the Goldbach conjecture were inseparable from the shadow of the circle method.

Of course, whether to study the Goldbach conjecture specifically requires a study of the circle method.

See if some results can be obtained.

Time has passed quietly.

…

Next, Xiao Yi's life in Santa Barbara is basically only about research.

After a few days, they completely solved all the remaining small problems of the Landau-Siegel zero conjecture.

This also means that this conjecture has been completely proved by them!

And the final result is not beyond their expectations, that is, there is no Landau-Siegel zero!

Chapter 129 Don't study physics

"Finally done."

When all the formulas on the blackboard finally return to the last result.

【L(1, χ)(log D)^2022】

Zhang Yitang standing in front of him sighed.

"In general, we proved that the lower bound of L(1, χ) is related to the distribution of zeros of a type of Dirichlet L-function in a certain area, and derived some results about the gaps between consecutive zeros. Finally, we evaluated some discrete means of the large sieve type, in which your circle method expansion was mainly used."

The technique that Xiao Yi used to introduce the circle method into their problem research using Xiao's expansion was temporarily called the circle method expansion by them.

"And now we have also proved that L(1, χ) is too small, thus obtaining an irreconcilable contradiction."

"So - Landau-Siegel zero does not exist."

Zhang Yitang turned his head to look at Xiao Yi next to him and sighed: "It's over."

His eyes were full of emotion.

His research on this conjecture happened many years ago.

Even earlier than when he studied the twin prime conjecture.

In his words, his breakthrough in the twin prime conjecture was just the result of a flash of inspiration, and his research on the Landau-Siegel zero-point conjecture has been with him for more than 20 years.

From a time when he was still unknown, he has now become a top scholar in the field of analytic number theory.

And finally, this question was answered today.

Of course, he knew very well that all of this was inseparable from Xiao Yi's help.

Looking at the young man in front of me...

It really always brings surprises to people.

Xiao Yi nodded slightly and said, "Yes, it's over."

Then he smiled and said: "It's a bit of a pity that it didn't prove to exist in the end. Otherwise, we might have gotten a million US dollars."

As long as it is proved that the zero point exists, it is equivalent to proving that the Riemann Hypothesis is wrong.

In this way, you can get 1 million US dollars provided by the Clay Institute. The seven major mathematical problems of the millennium are officially proposed by the Clay Institute. If you solve any of them, you can get 100 US dollars provided by the Clay Institute. Thousand dollar reward.

Hearing this, Zhang Yitang suddenly laughed and said: "If this is the case, it is not a pity, but a tragedy."

"Probably the entire mathematical world will be shaken by this."

Once the Riemann Hypothesis is proven wrong, quite a few mathematicians may have their lifelong beliefs shattered.

However, Xiao Yi seemed indifferent to this. He shrugged and said: "Whether the Riemann Hypothesis is correct or wrong, it cannot change just because we want it to be."

"Just like that sentence, objectively existing things are not subject to human will."

"If we really prove the existence of the Siegel zero point, I think the mathematical community should be happy about it."

"After all, this shows that there may be more to our mathematics than we imagine."

Zhang Yitang was startled, then nodded with a smile: "You're right. It's probably like the physics community. If they discover something beyond their experience, they may only be happy."

Hearing what Zhang Yitang said, Xiao Yi, who didn't know much about the physics world, couldn't help but become interested and asked: "Oh? Why is this?"

Zhang Yitang smiled and said: "You should know about the two dark clouds in physics."

Xiao Yi nodded and said: "Of course I know, it was mentioned in the high school physics textbook."

Zhang Yitang nodded: "Then the great physicists of the 20th century that you have heard about in textbooks all became great physicists because they studied these two dark clouds."

"For example, Einstein, Planck, Fermi, Bohr, etc. are all like this."

Xiao Yi was startled, but he quickly understood the reason.

"In other words, for the physics community, the more something is beyond their experience, the more it means that something has been hidden that has never been discovered before, which means that some important results can be discovered from it?"

"That's about it." Zhang Yitang raised his eyebrows, but he didn't expect Xiao Yi to react very quickly to this kind of thing.

"Now the physics community is lamenting that they have not had any major breakthroughs in many years. Of course, these are basically unsolvable things that can be studied. They have been studied in the last century. The problems left to this century are Each one is more troublesome than the other.”

"For example, what are vacuum catastrophes, dark matter, dark energy, or black holes, etc., and to a higher level, the multi-dimensional universe, string theory and so on."

Zhang Yitang laughed and said: "These things sound more sci-fi than the last. With the current level of human technology, it is basically unrealistic to solve these problems. Things that can be studied at least, such as something called Regarding the Higgs particle, in order to verify the existence of this particle, those physicists spent tens of billions to build a particle collider, which is the LHC.”