CM values and central L-values of elliptic modular forms |
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Authors: | Atsushi Murase |
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Institution: | 1. Department of Mathematical Science, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8555, Japan
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Abstract: | Let f be a holomorphic cusp form of weight l on SL2(Z) and Ω an algebraic Hecke character of an imaginary quadratic field K with Ω((α)) = (α/|α|) l for ${\alpha\in K^{\times}}Let f be a holomorphic cusp form of weight l on SL2(Z) and Ω an algebraic Hecke character of an imaginary quadratic field K with Ω((α)) = (α/|α|)
l
for a ? K×{\alpha\in K^{\times}}. Let L(f, Ω; s) be the Rankin-Selberg L-function attached to (f, Ω) and P(f, Ω) an “Ω-averaged” sum of CM values of f. In this paper, we give a formula expressing the central L-values L(f, Ω; 1/2) in terms of the square of P(f, Ω). |
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