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CM values and central L-values of elliptic modular forms

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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 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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  1. Department of Mathematical Science, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8555, Japan

    Atsushi Murase

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  1. Atsushi Murase
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Murase, A. CM values and central L-values of elliptic modular forms. Math. Ann. 347, 529–543 (2010). https://doi.org/10.1007/s00208-009-0447-0

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  • DOI: https://doi.org/10.1007/s00208-009-0447-0

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