JournalsjemsVol. 12, No. 5pp. 1097–1116

The second moment of quadratic twists of modular -functions

  • Kannan Soundararajan

    Stanford University, USA

  • Matthew P. Young

    Texas A&M University, College Station, USA
The second moment of quadratic twists of modular $L$-functions cover
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Abstract

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. 1097–1116

DOI 10.4171/JEMS/224