A Note on the Growth of Nearly Holomorphic Vector-valued Siegel Modular Forms
نویسندگان
چکیده
Let F be a nearly holomorphic vector-valued Siegel modular form of weight ρ with respect to some congruence subgroup of Sp2n(Q). In this note, we prove that the function on Sp2n(R) obtained by lifting F has the moderate growth (or “slowly increasing”) property. This is a consequence of the following bound that we prove: ‖ρ(Y )F (Z)‖ ∏n i=1(μi(Y ) λ1/2 + μi(Y ) −λ1/2) where λ1 ≥ . . . ≥ λn is the highest weight of ρ and μi(Y ) are the eigenvalues of the matrix Y .
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