The third moment of quadratic $L$-Functions

I will present a smoothed asymptotic formula for the third moment of Dirichlet $L$-functions associated to real characters. Beyond the main term, which was known, the formula has an unexpected secondary term of size $x^{3/4}$ and an error of size $x^{2/3}$. I will give background on the multiple Dirichlet series techniques that motivated this result. And I will describe the new ideas about local and global multiple Dirichlet series that made the final, sieving step in the proof possible. This is joint work with Adrian Diaconu.