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ma3150:2019v:start [2019-04-12] seip [Exam, dates and location] |
ma3150:2019v:start [2023-01-12] seip [Exercises] |
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Linje 9: | Linje 9: | ||
===== Lecturer ===== | ===== Lecturer ===== | ||
- | Kristian Seip: Office 956 in SB II, kristian.seip@ntnu.no | + | Kristian Seip: Office 956 in SB II, <kristian.seip@ntnu.no> |
===== Lectures ===== | ===== Lectures ===== | ||
Linje 30: | Linje 30: | ||
The final lecture took place on March 19. You are supposed to work on the topic for your oral presentation during the four remaining weeks of the semester. | The final lecture took place on March 19. You are supposed to work on the topic for your oral presentation during the four remaining weeks of the semester. | ||
- | ===== Reference Group ===== | ||
- | [[torkrin@pm.me|Tor Kringeland]] | ||
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- | [[larsmagnus.overlier@gmail.com|Lars Magnus Øverlier]] | ||
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- | * {{ : | ||
===== Contents of the lectures ===== | ===== Contents of the lectures ===== | ||
Linje 70: | Linje 64: | ||
You are welcome to work on the exercises in room 1329 SB2 on Friday 14: | You are welcome to work on the exercises in room 1329 SB2 on Friday 14: | ||
- | * Exercise 1, from Apostol: 2.1, 2.2, 2.6, 2.21, 2.26, 3.1, 3.2, 3.4, 3.5, 4.7, 4.18, 4.19 (a) (guidance offered on January 18 and 25). {{ : | + | * Exercise 1, from Apostol: 2.1, 2.2, 2.6, 2.21, 2.26, 3.1, 3.2, 3.4, 3.5, 4.7, 4.18, 4.19 (a) (guidance offered on January 18 and 25). |
* {{ : | * {{ : | ||
* Exercise 3, from Apostol: 11.1 (a)--(d), 11.3, 13.2 (observing that \( A(x)=\pi(x)+\pi(x^{1/ | * Exercise 3, from Apostol: 11.1 (a)--(d), 11.3, 13.2 (observing that \( A(x)=\pi(x)+\pi(x^{1/ | ||
Linje 80: | Linje 74: | ||
As part of the oral exam, the students should give short presentations of topics assigned to them. These are topics that are not covered by the lectures. You may choose a topic yourself (to be approved by me) or choose one from the following list: | As part of the oral exam, the students should give short presentations of topics assigned to them. These are topics that are not covered by the lectures. You may choose a topic yourself (to be approved by me) or choose one from the following list: | ||
- | - Mertens' | + | - Mertens' |
- | - The Bertrand--Chebyshev theorem, including Ramanujan and Erdős' | + | - The Bertrand--Chebyshev theorem, including Ramanujan and Erdős' |
- Ramanujan primes (chosen by '' | - Ramanujan primes (chosen by '' | ||
- | - Skewes' | + | - Skewes' |
- General distribution of nontrivial zeros of \(\zeta(s)\) | - General distribution of nontrivial zeros of \(\zeta(s)\) | ||
- | - Zeros on the critical line, including density results | + | - Zeros on the critical line, including density results |
- The error term in the prime number theorem and zero-free regions | - The error term in the prime number theorem and zero-free regions | ||
- The Lindelöf hypothesis and the density hypothesis | - The Lindelöf hypothesis and the density hypothesis | ||
- | - Mean value theorems - results and conjectures | + | - Mean value theorems - results and conjectures |
- Zeta functions for which RH fails | - Zeta functions for which RH fails | ||
- | - Dirichlet' | + | - Dirichlet' |
- | - Elementary sieve methods and Brun's theorem on twin primes | + | - Elementary sieve methods and Brun's theorem on twin primes |
- Voronin' | - Voronin' | ||
- | - Lagarias' | + | - Lagarias' |
- The Beurling--Nyman condition for RH | - The Beurling--Nyman condition for RH | ||
- | - Li's criterion for RH (chosen by '' | + | - Li's criterion for RH |
- | - The Bohr--Cahen formulas for abscissas of convergence and the growth of \(\sum_{n\le x} \mu(n)\). | + | - The Bohr--Cahen formulas for abscissas of convergence and the growth of \(\sum_{n\le x} \mu(n)\). |
- Alternate proofs of the functional equation for \( \zeta(s)\) (Titchmarsh gives 7 proofs; take a look and make your own selection of some of them) | - Alternate proofs of the functional equation for \( \zeta(s)\) (Titchmarsh gives 7 proofs; take a look and make your own selection of some of them) | ||
- Approximations of \(\zeta(s)\), | - Approximations of \(\zeta(s)\), | ||
- | - The Riemann--Weil explicit formula | + | - The Riemann--Weil explicit formula |
- Siegel zeros. | - Siegel zeros. | ||
Linje 108: | Linje 102: | ||
===== Exam, dates and location ===== | ===== Exam, dates and location ===== | ||
- | The oral presentations will be given on May 8. **You are strongly encouraged to be present at all the presentations!** Oral examinations will take place on May 9. Both events will take place in Room 656 SB2. A detailed schedule is as follows. | + | The oral presentations will be given on May 8. **You are strongly encouraged to be present at all the presentations!** Oral examinations will take place on May 9. Both events will take place in Room 656 SB2. |
- | + | ||
- | === Schedule May 8 === | + | |
- | + | ||
- | * 08:30 - 08:55 '' | + | |
- | * 09:00 - 09:25 '' | + | |
- | * 09:30 - 09:55 '' | + | |
- | * 10:00 - 10:25 '' | + | |
- | * 10:30 - 10:55 '' | + | |
- | * 11:00 - 11:25 '' | + | |
- | * 11:30 - 11:55 '' | + | |
- | * 13:00 - 13:25 '' | + | |
- | * 13:30 - 13:55 '' | + | |
- | * 14:00 - 14:25 '' | + | |
- | * 14:30 - 14:55 '' | + | |
- | + | ||
- | === Schedule May 9 === | + | |
- | + | ||
- | * 08:30 - 08:55 '' | + | |
- | * 09:00 - 09:25 '' | + | |
- | * 09:30 - 09:55 '' | + | |
- | * 10:00 - 10:25 '' | + | |
- | * 10:30 - 10:55 '' | + | |
- | * 11:00 - 11:25 '' | + | |
- | * 11:30 - 11:55 '' | + | |
- | * 13:00 - 13:25 '' | + | |
- | * 13:30 - 13:55 '' | + | |
- | * 14:00 - 14:25 '' | + | |
- | * 14:30 - 14:55 '' | + | |
Linje 145: | Linje 110: | ||
You may in principle come at " | You may in principle come at " | ||
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