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ma3150:2019v:start [2019-04-12]
seip [Exam, dates and location] 		ma3150:2019v:start [2020-12-29]
hallvabo GDPR
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 ===== 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 =====
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 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]] 
- 
-[[larsmagnus.overlier@gmail.com|Lars Magnus Øverlier]] 
- 
-  * {{ :ma3150:2019v:report_refgroup_jan14-2019.pdf |Minutes}} from the first meeting January 14. 
 ===== Contents of the lectures ===== ===== Contents of the lectures =====
  
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's theorems and Mertens's constant (chosen by ''Tor Kringeland'')  +  - Mertens's theorems and Mertens's constant 
-  - The Bertrand--Chebyshev theorem, including Ramanujan and Erdős's work on it (chosen by ''Claudia Wohlgemuth'')+  - The Bertrand--Chebyshev theorem, including Ramanujan and Erdős's work on it
   - Ramanujan primes (chosen by ''Oskar Vikhamar-Sandberg'')   - Ramanujan primes (chosen by ''Oskar Vikhamar-Sandberg'')
-  - Skewes's number and sign changes in \( \pi(x)-\operatorname{li}(x) \) (chosen by ''Knut Bjarte Haus'')+  - Skewes's number and sign changes in \( \pi(x)-\operatorname{li}(x) \)
   - General distribution of nontrivial zeros of \(\zeta(s)\)    - General distribution of nontrivial zeros of \(\zeta(s)\) 
-  - Zeros on the critical line, including density results (chosen by ''Terje Bull Karlsen'')+  - 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 (chosen by ''Fredrik Vaagen'')+  - Mean value theorems - results and conjectures
   - Zeta functions for which RH fails    - Zeta functions for which RH fails 
-  - Dirichlet's divisor problem, including Voronoi's summation formula (chosen by ''Lars Magnus Øverlier'') +  - Dirichlet's divisor problem, including Voronoi's summation formula 
-  - Elementary sieve methods and Brun's theorem on twin primes (chosen by ''Daniel Olaisen'')+  - Elementary sieve methods and Brun's theorem on twin primes
   - Voronin's universality theorem and value distribution of the Riemann zeta function    - Voronin's universality theorem and value distribution of the Riemann zeta function 
-  - Lagarias's version of Guy Robin's criterion (chosen by Morten ''Ravnemyr'')   +  - Lagarias's version of Guy Robin's criterion
   - The Beurling--Nyman condition for RH    - The Beurling--Nyman condition for RH 
-  - Li's criterion for RH (chosen by ''William Tell'') +  - 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 \(\zeta(s)\), including the approximate functional equation   - Approximations of \(\zeta(s)\), including the approximate functional equation
-  - The Riemann--Weil explicit formula (chosen by ''Henrik Romnes'')+  - 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 ''Tor Kringeland'': Mertens's theorems and Mertens's constant  +
-  * 09:00 - 09:25 ''Claudia Wohlgemuth'': The Bertrand--Chebyshev theorem, including Ramanujan and Erdős's work on it  +
-  * 09:30 - 09:55 ''Oskar Vikhamar-Sandberg'': Ramanujan primes +
-  * 10:00 - 10:25 ''Knut Bjarte Haus'': Skewes's number and sign changes in \( \pi(x)-\operatorname{li}(x) \)  +
-  * 10:30 - 10:55 ''Terje Bull Karlsen'': Zeros on the critical line, including density results +
-  * 11:00 - 11:25 ''Lars Magnus Øverlier'': Dirichlet's divisor problem, including Voronoi's summation formula +
-  * 11:30 - 11:55 ''Fredrik Vaagen'': Mean value theorems - results and conjectures +
-  * 13:00 - 13:25 ''William Tell'': Li's criterion for RH +
-  * 13:30 - 13:55 ''Morten Ravnemyr'': Lagarias's version of Guy Robin's criterion +
-  * 14:00 - 14:25 ''Daniel Olaisen'': Elementary sieve methods and Brun's theorem on twin primes +
-  * 14:30 - 14:55 ''Henrik Romnes'': The Riemann–Weil explicit formula. +
- +
-=== Schedule May 9 === +
- +
-  * 08:30 - 08:55 ''Tor Kringeland'' +
-  * 09:00 - 09:25 ''Claudia Wohlgemuth'' +
-  * 09:30 - 09:55 ''Oskar Vikhamar-Sandberg'' +
-  * 10:00 - 10:25 ''Knut Bjarte Haus''  +
-  * 10:30 - 10:55 ''Terje Bull Karlsen'' +
-  * 11:00 - 11:25 ''Lars Magnus Øverlier'' +
-  * 11:30 - 11:55 ''Fredrik Vaagen'' +
-  * 13:00 - 13:25 ''William Tell'' +
-  * 13:30 - 13:55 ''Morten Ravnemyr'' +
-  * 14:00 - 14:25 ''Daniel Olaisen'' +
-  * 14:30 - 14:55 ''Henrik Romnes'' +
  
  
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 You may in principle come at "any" time during the days I am in my office, but I would recommend that you contact me in advance to make an appointment.   You may in principle come at "any" time during the days I am in my office, but I would recommend that you contact me in advance to make an appointment.  
- 
- 
  
  
2023-02-16, Kristian Seip