Chapter 229

The question session of the defense teacher is known as the most important part of the three links of the defense, and it is also called the "ghost gate" by countless graduates.

Extremely difficult questions keep throwing at you like a cannon, and you have to muster up the energy to face it with a smile.

Especially the kind of questions that sound confused, it makes people want to answer, and they don't know how to speak.

There are two types of questions in the graduation defense.

One is that the tutor takes the lead in asking questions, and for each question, the candidate has about five to ten minutes to prepare.

After you have prepared your questions, you will answer the questions.

On the other hand, it is more of a test of students' academic level.

That is, the teacher of the defense team asks questions on the spot, and the students answer on the spot, without any preparation time, even a minute.

This form is undoubtedly extremely cruel to the students participating in the defense, but it is the most effective test of their four-year undergraduate studies.

However, considering the graduation rate, half of the defense questions of the Yan University School of Mathematics were a mixture of two question forms.

Two questions are given time for students to prepare their words.

The other two questions are a complete test of students' performance.

…………

In the defense classroom, Gu Lu was casually flipping through Shao Yuan's graduation thesis, and looked at Shao Yuan on the stage with peaceful eyes.

Gu Lu smiled slightly, "Shao Yuan, next I will ask a few questions about your graduation thesis." ”

Shao Yuan swallowed his saliva fiercely, looking like he was facing a great enemy.

"Are you ready?"

"Accurate, ready. ”

The most common questions in the graduation defense are generally broad questions such as 'Why did you choose this topic?' or 'What is the meaning and purpose of researching this topic?'.

But Gu Lu obviously wouldn't ask such a regular question.

Gu Lu asked a completely professional question.

"Shao Yuan, since the topic you chose is the Rankin-Selberg method to study the L-function of the Fourier coefficients of two modular forms, similarly, on page 15 of the paper, you also mentioned that the Rankin-Selberg method can also be applied to the study of Maass form. ”

So, you can briefly tell me about the application of the Rankin-Selberg method to the specific study of the Maass form. ”

How does the Rankin-Selberg method apply to Maass form studies?

Shao Yuan was stunned on the spot.

This one......

I don't know!

At that time, when he was looking up the relevant materials about the 'Rankin-Selberg method', he happened to see this sentence, so he directly copied it.

But who would have thought that Gu Lu would ask this question!

The expression on his face was entangled for a long time, and Shao Yuan replied in a whisper, "Teacher, I won't." ”

"Okay, let's go next. Gu Lu didn't say much, and asked the next question directly.

Gu Lu knocked on the table and turned Shao Yuan's graduation thesis in front of him to one of the pages, "On the eighteenth page of the thesis, you mentioned the one-time mean of a class of L-functions at the special point sj=1/2ttj, which proves that when T approaches positive infinity, there is a formula ∑wjL(1/2+itQ*uj)e^(-t/2)=2π^(-2)T^2+O(T(logT)^9) that holds. ”

"Shao Yuan, can you give me the specific proof process of the formula!"

Gu Lu's eyes were still looking at Shao Yuan peacefully.

Shao Yuan was dumbfounded again.

Stunned on the spot, a pair of eyes looked at Gu Lu in a daze.

This question, Shao Yuan still won't.

Such a complex progressive formula, when writing the paper, Shao Yuan also directly copied it from a foreign literature.

As for the specific proof process, Shao Yuan did not look at it in detail.

This caused him to be unable to answer Gu Lu's question.

Unable to answer two questions in a row, Shao Yuan was already hopeless about his defense results.

It was obviously a hot day, but fine cold sweat oozed from Shao Yuan's forehead.

"Don't worry, I'll give you ten minutes to think, and I'll give you an answer in ten minutes. Gu Lu added with a smile.

The key is to give me ten minutes, and I won't either!

Shao Yuan was about to cry.

Obviously, the difficulty of this problem cannot be solved in ten minutes.

"Teacher, I don't know this question. Shao Yuan lowered his head and opened his mouth with a weak mosquito chirping.

"However, teacher, I want to know the steps to prove this formula!" Shao Yuan raised his head and looked at Gu Lu with a sincere gaze.

Gu Lu shrugged his shoulders and smiled, "Yes." ”

Then, Gu Lu got up and stood up, picked up a piece of chalk, and without any hesitation, wrote down the formula on the blackboard.

【From n ≥ 3 and 2n/3 2n, so there is only i = 1 term in the summing formula, i.e.: s = floor(2n/p)- 2floor(n/p). Due to 2n/3 < p ≤ n also indicates 1 ≤ n/p < 3/2, so s = floor(2n/p)- 2floor(n/p)......]

【…… θ(n)≡Σp≤n log(p)&lt; n log4，…… In summary, we can get Πp≤N p =(Πp≤m+1 p)(Πm+1< p≤2m+1 p)&lt; 4m+1 4m = 42m+1 = 4N。 Therefore, it can be proved ∑that wjL(1/2+itQ*uj)e^(-t/2)=2π^(-2)T^2+O(T(logT)^9)!]

Gu Lu's speed of writing is so fast that Shao Yuan's thinking can't keep up with Gu Lu's speed of writing.

So much so that Shao Yuan couldn't finish reading the five-element formula, and Gu Lu had already finished the entire proof process.

However, looking at the frequent nodding of the other two teachers below, Shao Yuan knew that there should be no mistakes in the answers written by Gu Lu.

After writing, Gu Lu returned to his seat directly, and then looked at Shao Yuan with a smile, "After the defense is over, you can take pictures and take a full look, now, I will ask you the third question." ”

"The inference 10 drawn on page 15 of your paper, the specific reasoning steps are too brief, can you prove it again with a specific formula on the spot?" Gu Lu asked with a smile.

Silence, silence is Cambridge tonight.

After being silent for a long time, Shao Yuan blushed and said, "Yes, but I need a little time." ”

Gu Lu nodded, "No problem." ”

After performing the calculations on the scratch paper for a while, Shao Yuan performed the deduction steps on the blackboard.

Glancing at the formula given by Shao Yuan, Gu Lu nodded with satisfaction.

This student, the strength is still a little.

Then, Gu Lu turned his head to look at Teacher Zhang beside him, "Teacher Zhang, this last question is up to you, right?"

Teacher Zhang nodded with a smile, "Yes, no problem." ”

What relieved Shao Yuanda, who was nervous on the stage, was that the question asked by this teacher Zhang was not as perverted as the teacher just now.

Shao Yuan finished the question in a regular manner.

"Wait until we discuss your results. Gu Lu reminded Shao Yuan, and then talked to Teacher Zhang and Teacher Shi in a low voice.

Shao Yuan's heart was nervous.

The nine students waiting in the back row were also uncomfortable, and when they saw that the questions of this defense were so difficult, several of them began to tremble with nervousness.

However, when Gu Lu said the result of the discussion, the students in the classroom breathed a sigh of relief.

Shao Yuan still passed the graduation defense unanimously as he wished.

Even if the process is not very good.