JournalsjemsVol. 23, No. 6pp. 2051–2070

# On the third moment of .css-nii8vn .katex{font-size:1.07em;}$L(\frac{1}{2}, \chi_{d})$ {II}: the number field case

University of Minnesota, Minneapolis, USA

Swarthmore College, USA We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet $L$-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 $\delta > 0.$
Adrian Diaconu, Ian Whitehead, On the third moment of $L(\frac{1}{2}, \chi_{d})$ {II}: the number field case. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 2051–2070
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