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L-functions of second-order cusp forms |
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| Authors: | N. Diamantis M. Knopp G. Mason C. O’Sullivan |
| Affiliation: | (1) School of Mathematical Sciences, University of Nottingham, University Park, NG7 2RD, United Kingdom;(2) Department of Mathematics, Temple University, Philadelphia, Pennsylvania, 19122-2585;(3) Mathematics Department, University of California Santa Cruz, 194 Baskin Engineering, Santa Cruz, California, 95064;(4) Department of Math & Computer Science, Bronx Community College of the City University of New York, University Ave. at West 181 St., Bronx, New York, 10453 |
| 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. 2000 Mathematics Subject Classification Primary—11F12, 11F66 G. Mason: Research supported in part by NSF Grant DMS 0245225. C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34. |
| Keywords: | L-functions Converse theorems Cuspforms Second-order automorphic forms |
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