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On the third moment of $L(\tfrac{1}{2}, χ_d)$ II: the number field case (1804.00690v1)

Published 2 Apr 2018 in math.NT

Abstract: We establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet $L$-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size $x{\frac{3}{4}}$. The error term in the asymptotic formula is on the order of $O(x{\frac{2}{3}+\delta})$ for every $\delta > 0.$

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