Department of

January 2020February 2020March 2020 Su Mo Tu We Th Fr Sa Su Mo Tu We Th FrSaSu Mo Tu We Th Fr Sa 1 2 3 4 1 1 2 3 4 5 6 7 5 6 7 8 9 10 11 2 3 4 5 6 7 8 8 9 10 11 12 13 14 12 13 14 15 16 17 18 9 10 11 12 13 14 15 15 16 17 18 19 20 21 19 20 21 22 23 24 25 16 17 18 19 20 21 22 22 23 24 25 26 27 28 26 27 28 29 30 31 23 24 25 26 27 282929 30 31

Thursday, February 20, 2020

**Abstract:** 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.