We study the second moment of the central values of quadratic twists of a modular L-function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.
Cite this article
Kannan Soundararajan, Matthew P. Young, The second moment of quadratic twists of modular -functions. J. Eur. Math. Soc. 12 (2010), no. 5, pp. 1097–1116DOI 10.4171/JEMS/224