Send the lecturer (R. Hough) email at:
Office: 4-107 Mathematics Building
Office hours: 6-7pm Thursday in the MLC, 2-4pm, Friday in 4-107.
Lectures: TuTh 3:30-4:50pm Physics P123
This course combines an introduction to analytic number theory with a selection of modern topics in prime and combinatorial number theory. Roughly the first third of the course will cover the Prime Number Theorem in arithmetic progressions, following the treatment of Davenport's Multiplicative number theory. The remaining topics are to include Maynard's proof of bounded gaps between primes, and the Green-Tao Theorem on arbitrarily long arithmetic progressions in the primes.
| 1. | Davenport Chap. 1 | Primes in arithmetic progressions |
| 2. | Davenport Chap. 2-3 | Gauss sums, cyclotomy |
| 3. | Davenport Chap. 4-5 | Primes in arithmetic progressions, primitive characters |
| 4. | Davenport Chap. 6 | Dirichlet's Class Number Formula |
| 5. | Davenport Chap. 7-9 | The distribution of primes, Riemann's memoir, the functional equation |
| 6. | Davenport Chap. 10-12 | Properties of the Gamma function, integral functions of order 1, the infinite product representations |
| 7. | Davenport Chap. 13-14 | The classical zero free region |
| 8. | Davenport Chap. 15-17 | The zero counting functions, and the explicit formula |
| 9. | Davenport Chap. 18-20 | The prime number theorem, PNT in AP I |
| 10. | Davenport Chap. 21-22 | Siegel's theorem, PNT in AP II |
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