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

Adrian Diaconu; Ian Whitehead

doi:10.4171/jems/1049

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

On the third moment of $L (\frac{1}{2}, χ_{d})$ {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$

Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

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 $O (x^{\frac{2}{3} + δ})$ for every $δ > 0.$

Cite this article

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

DOI 10.4171/JEMS/1049