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

On the third moment of L(12,χd)L(\frac{1}{2}, \chi_{d}) {II}: the number field case

  • Adrian Diaconu

    University of Minnesota, Minneapolis, USA
  • Ian Whitehead

    Swarthmore College, USA
On the third moment of $L(\frac{1}{2}, \chi_{d})$ {II}: the number field case cover
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Abstract

We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet LL-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size x34.x^{\frac{3}{4}}. The error term in the asymptotic formula is on the order of O(x23+δ)O(x^{\frac{2}{3}+\delta}) for every δ>0.\delta > 0.

Cite this article

Adrian Diaconu, Ian Whitehead, On the third moment of L(12,χd)L(\frac{1}{2}, \chi_{d}) {II}: the number field case. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 2051–2070

DOI 10.4171/JEMS/1049