Assignments

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