On the Average Growth of Fouriercoefficients of Siegel Cusp Forms of Genus
نویسنده
چکیده
Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp 2 (Z) of genus 2 and denote by a(T) (T 2 Q (2;2) ; T > 0 half-integral) its Fourier coeecients. It is known (see BB ocherer & Raghavan, 1988 and Fomenko, 1987) that (1) X fT>0; det(T)=N g=GL2(Z) ja(T)j 2 ";F N k?3=32+" (" > 0) where the sum is over GL 2 (Z)-classes of T > 0 with det(T) = N: In the present note we shall give a result on the average growth of ja(T)j 2 ; where the average is taken w.r.t. the trace.
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تاریخ انتشار 1997