PROBLEM SET # | PROBLEMS | DUE DATES |
---|---|---|

1 | Exercises 1-8 from the prime number theorem (PDF) | Lec #4 |

2 | Exercises 1-10 from Dirichlet series and arithmetic functions (PDF) | Lec #7 |

3 | Exercises 1-5 from Dirichlet characters and Dirichlet L-functions (PDF) Exercises 1-6 from primes in arithmetic progressions (PDF) | Lec #10 |

4 | Exercises 1-5 from the functional equation for the Riemann zeta function (PDF) Exercises 1-4 from the functional equations for Dirichlet L-functions (PDF) | Lec #13 |

5 | Exercises 5-9 from the functional equations for Dirichlet L-functions (PDF) Exercise 1 from error bounds in the prime number theorem (PDF) Exercises 1-6 from more on the zeroes of zeta (PDF) | Lec #17 |

6 | Exercises 1-4 from von Mangoldt's formula (PDF) Exercises 1-6 from revisiting the sieve of Eratosthenes (PDF) | Lec #20 |

7 | Exercises 1-2 from Brun's combinatorial sieve (PDF) Exercises 1-5 from the Selberg sieve (PDF) | Lec #23 |

8 | Exercises 6-9 from the Selberg sieve (PDF) Exercises 1-5 from applying the Selberg sieve (PDF) | Lec #25 |

9 | Exercises 1-4 from introduction to large sieve inequalities (PDF) Exercises 1-3 from a multiplicative large sieve inequality (PDF) | Lec #27 |

10 | Exercises 1-2 from the Bombieri-Vinogradov theorem (statement) (PDF) Exercises 1-5 from the Bombieri-Vinogradov theorem (proof) (PDF) | Lec #30 |

11 | Exercises 1-5 from prime k-tuples (PDF) Exercises 1-3 from short gaps between primes (after Goldston-Pintz-Yildirim) (PDF) | Lec #33 |