Doklady Mathematics

, Volume 92, Issue 1, pp 417–420 | Cite as

On the second moment of L-series of holomorphic cusp forms on the critical line

Mathematics

Abstract

New uniform estimates are obtained for the second moment of L-series of cusp forms of even weight 2k ≥ 4 with respect to the congruence subgroup Γ0(N).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Iwaniec and E. Kowalski, Analytic Number Theory (Am. Math. Soc., Providence, R.I., 2004; MTsNMO, Moscow, 2014).Google Scholar
  2. 2.
    A. Good, Mathematika 29, 278–295 (1982).MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Jutila and Y. Motohashi, Acta Math. 195, 61–115 (2005).MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    V. Blomer and G. Harcos, J. Reine Angew. Math. 621, 53–79 (2008).MATHMathSciNetGoogle Scholar
  5. 5.
    A. Sankaranarayanan, Hardy-Ramanujan J. 26, 2–17 (2003).MATHMathSciNetGoogle Scholar
  6. 6.
    V. A. Bykovskii, J. Math. Sci. 89 (1), 915–932 (1998).MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. A. Bykovsky, in Number Theory in Progress (Walter de Gruyter, Berlin, 1999), pp. 675–689.Google Scholar
  8. 8.
    Higher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdelyi (McGraw-Hill, New York, 1953; Nauka, Moscow, 1966), Vol. 2.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Institute of Applied Mathematics (Khabarovsk Branch), Far Eastern BranchRussian Academy of SciencesKhabarovskRussia

Personalised recommendations