**Time:** Thursday 17:00-19:30

**Place:** Y27H12, Irchel campus

**Email:** brad.rodgersmath.uzh.ch, or nicolas.roblesmath.uzh.ch

**Course webpage with syllabus:** http://www.math.uzh.ch/index.php?ve_se_det&key2=869

**Books:** There are a large number of books on analytic number theory. Some useful resources include but are not limited to:

- T. Apostol,
*Introduction to Analytic Number Theory*. - G.H. Hardy and E.M. Wright,
*Introduction to the Theory of Numbers* - S. J. Miller and R. Takloo-Bighash,
*An Invitation to Modern Number Theory* - H. Rademacher,
*Lectures on Elementary Number Theory* - (More advanced) H. Montgomery and R. Vaughan,
*Multiplicative Number Theory I: Classical Theory*

- Chapter 10 and 11 of G. Shilov,
*Elementary Real and Complex Analysis*

**A (tentative) calendar of talks. This may be subject to change.**

- Sept. 18 - No class
- Sept. 25 - Some fundamentals of number theory (Nicolas)
- Oct. 2 - Some more fundamentals, and arithmetic functions (Nicolas)
- Oct. 9 - Modular arithmetic (Milan)
- Oct. 16 - Quadratic reciprocity (Tania)
- Oct. 23 - Review of complex analysis, and Chebyshev bounds (Brad/Nicolas)
- Oct. 30 - Dirichlet characters (Benjamin)
- Nov. 6 - General Dirichlet Series (Adrienne, 40 min) / Introduction to the Riemann zeta function (Roland, 40 min)
- Nov. 13- Dirichlet's theorem (Andrea 60 min) / Dirichlet's hyperbola trick (Cagla 20 min)
- Nov. 20 - Prime number theorem (Paulo 60 min) / Dirichlet's hyperbola trick (Cagla 20 min)
- Nov. 27 - Twin primes and Brun's constant (Alessandro/Gianluca)
- Dec. 4 - Elliptic curves (Violetta/Dario)
- Dec. 11 - Erdős-Kac theorem (Robert)
- Dec. 18 - Zeros on the critical line: Hardy's theorem (Francesca/Eduardo)

**Evaluation:**

- This class is a pass/fail class.
- Each participant is required to present a talk on a topic of their choice (related to analytic number theory), and hand in a short written version of their talk.