Kyoto Journal of Mathematics

Central critical values of modular Hecke L-functions

Haruzo Hida

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Abstract

We give an explicit formula for the central critical value L(1/2,π̂χ) of the base-change lift π̂ to an imaginary quadratic field K of an automorphic representation π as the square of a finite sum of the values of a nearly holomorphic cusp form in π at elliptic curves with complex multiplication by K. As long as the transcendental factor of the value is a CM period, χ is basically any unitary arithmetic Hecke character of K inducing the inverse of the central character of π.

Article information

Source
Kyoto J. Math., Volume 50, Number 4 (2010), 777-826.

Dates
First available in Project Euclid: 29 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1291041218

Digital Object Identifier
doi:10.1215/0023608X-2010-014

Mathematical Reviews number (MathSciNet)
MR2740694

Zentralblatt MATH identifier
1271.11057

Subjects
Primary: 11F11: Holomorphic modular forms of integral weight 11F25: Hecke-Petersson operators, differential operators (one variable) 11F27: Theta series; Weil representation; theta correspondences 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Citation

Hida, Haruzo. Central critical values of modular Hecke $L$ -functions. Kyoto J. Math. 50 (2010), no. 4, 777--826. doi:10.1215/0023608X-2010-014. https://projecteuclid.org/euclid.kjm/1291041218


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References

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