**Title of the course:** Modular Forms and L functions in Analytic Number Theory

**Instructor:** Dr. Eren Mehmet Kıral

**Institution:** -

**Dates:** 6-12 August 2018

**Prerequisites:** Complex Analysis, Fourier analysis.

**Level:** Graduate, advanced undergraduate

**Abstract:**

**Day 1:** The Gauss Circle Problem, Voronoi Summation formula

**Day 2:** The jacobi theta function, every number can be written as a sum of four squares.

**Day 3:** The Riemann Zeta function, Riemann's memoir (a proof of Prime number theorem if Riemann Hypothesis were true)

**Day 4:** Kloosterman's original paper on representing integers by quadratic forms in four variables where a Kloosterman sum is first introduced

**Day 5:** Modular forms on the upper half plane, (for those also taking the Elliptic curve class) what did Andrew Wiles' modularity theorem which led to a proof of Fermat's Last Theorem actually say (no proof).

**Day 6:** Eisenstein series, Poincare series, Petersson Trace formula (more Kloosterman sums!). (Or some other topic you might ask during the week, but give me early notice)

**Language: **TR, EN