Pal, Aprameyo; de Vera-Piquero, Carlos

Pullbacks of Saito-Kurokawa Lifts and a Central Value Formula for Degree 6 \(L\)-Series

Doc. Math. 24, 1935-2036 (2019)
DOI: 10.25537/dm.2019v24.1935-2036
Communicated by Otmar Venjakob

Summary

We prove an explicit central value formula for a family of complex \(L\)-series of degree 6 for \(\text{GL}_2 \times \text{GL}_3\) which arise as factors of certain Garret-Rankin triple product \(L\)-series associated with modular forms. Our result generalizes a previous formula of Ichino involving Saito-Kurokawa lifts, and as an application we prove Deligne's conjecture stating the algebraicity of the central values of the considered \(L\)-series up to the relevant periods.

Mathematics Subject Classification

11F46, 11F30, 11F27, 11F67

Keywords/Phrases

central value formula, Saito-Kurokawa lifts, automorphic periods, Gross-Prasad conjecture

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Affiliation

Pal, Aprameyo
Fakultät für Mathematik, Universität Duisburg-Essen, Essen, Germany
de Vera-Piquero, Carlos
Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Spain

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