Abstract
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.
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2000 Mathematics Subject Classification Primary—11F12, 11F66
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Diamantis, N., Knopp, M., Mason, G. et al. L-functions of second-order cusp forms. Ramanujan J 12, 327–347 (2006). https://doi.org/10.1007/s11139-006-0147-2
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DOI: https://doi.org/10.1007/s11139-006-0147-2