Kyoto Journal of Mathematics

On mod p nonvanishing of special values of L-functions associated with cusp forms on GL2 over imaginary quadratic fields

Kenichi Namikawa

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Abstract

Let f be a cusp form on GL2 over an imaginary quadratic field F of class number 1, and let p be an odd prime which satisfies some mild conditions. Then we show the existence of a finite-order Hecke character φ of FA× such that the algebraic part of the special value of L-functions of fφ at s=1 is a p-adic unit. This is an analogous result to the result of A. Ash and G. Stevens for GL2 over the field of rationals obtained in [AS].

Article information

Source
Kyoto J. Math., Volume 52, Number 1 (2012), 117-140.

Dates
First available in Project Euclid: 19 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1329684745

Digital Object Identifier
doi:10.1215/21562261-1503782

Mathematical Reviews number (MathSciNet)
MR2892770

Zentralblatt MATH identifier
1284.11087

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture)

Citation

Namikawa, Kenichi. On mod $p$ nonvanishing of special values of $L$ -functions associated with cusp forms on $\operatorname{GL}_{2}$ over imaginary quadratic fields. Kyoto J. Math. 52 (2012), no. 1, 117--140. doi:10.1215/21562261-1503782. https://projecteuclid.org/euclid.kjm/1329684745


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References

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