Heegner points,cycles and Maass forms |
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| Authors: | Svetlana Katok Peter Sarnak |
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| Affiliation: | (1) Department of Mathematics, The Pennsylvania State University, 302 McAllister Building, 16802 University Park, PA, USA;(2) Department of Mathematics, Princeton University, Fine Hall, Washington Road, 08544-1000 Princeton, NJ, USA |
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| Abstract: | We derive for Hecke-Maass cusp forms on the full modular group a relation between the sum of the form at Heegner points (and integrals over Heegner cycles) and the product of two Fourier coefficients of a corresponding form of half-integral weight. Specializing to certain cycles we obtain the nonnegativity of theL-function of such a form at the center of the critical strip. These results generalize similar formulae known for holomorphic forms. Partially supported by NSF grant # DMS-9096262. Partially supported by NSF grant # DMS-9102082. |
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