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 and their connection to moments. If time permits, 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.

 

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