Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms
نویسندگان
چکیده
منابع مشابه
Rankin-selberg without Unfolding and Bounds for Spherical Fourier Coefficients of Maass Forms
We use the uniqueness of various invariant functionals on irreducible unitary representations of PGL2(R) in order to deduce the classical Rankin-Selberg identity for the sum of Fourier coefficients of Maass cusp forms and its new anisotropic analog. We deduce from these formulas non-trivial bounds for the corresponding unipotent and spherical Fourier coefficients of Maass forms. As an applicati...
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a r t i c l e i n f o a b s t r a c t Let f and g be Maass cusp forms for SL m (Z) and SL m (Z), respectively, with 2 ≤ m ≤ m. Let λ f ×g (n) be the normalized coefficients of L(s, f × g), the Rankin–Selberg L-function for f and g. In this paper the asymptotics of a Voronoi-type summation formula for λ f ×g (n) are derived. As an application estimates are obtained for the smoothly weighted aver...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2007
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-07-00581-4