The fourth moment of quadratic Dirichlet L-functions

Abstract

We study the fourth moment of quadratic Dirichlet L-functions at $$s= \frac{1}{2}$$ . We show an asymptotic formula under the generalized Riemann hypothesis, and obtain a precise lower bound unconditionally. The proofs of these results follow closely arguments of Soundararajan and Young (J Eur Math Soc 12(5):1097–1116, 2010) and Soundararajan (Ann Math (2) 152(2):447–488, 2000).