L-functions of second-order cusp forms
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.
KeywordsL-functions Converse theorems Cuspforms Second-order automorphic forms
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