The Ramanujan Journal

, Volume 12, Issue 3, pp 327–347 | Cite as

L-functions of second-order cusp forms

  • N. Diamantis
  • M. Knopp
  • G. Mason
  • C. O’Sullivan


We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we investigate the effect of adding an assumption of periodicity to this criterion.


L-functions Converse theorems Cuspforms Second-order automorphic forms 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • N. Diamantis
    • 1
  • M. Knopp
    • 2
  • G. Mason
    • 3
  • C. O’Sullivan
    • 4
  1. 1.School of Mathematical SciencesUniversity of NottinghamUniversity ParkUnited Kingdom
  2. 2.Department of MathematicsTemple UniversityPhiladelphia
  3. 3.Mathematics DepartmentUniversity of California Santa CruzSanta Cruz
  4. 4.Department of Math & Computer ScienceBronx Community College of the City University of New YorkBronx

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