Geodesic
Pullbacks of Saito-Kurokawa Lifts and a Central Value Formula for Degree 6 $L$-Series
Documenta mathematica, Tome 24 (2019), pp. 1935-2036.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11F46, 11F30, 11F27, 11F67
Keywords: central value formula, Saito-Kurokawa lifts, automorphic periods, Gross-Prasad conjecture 
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     author = {Pal, Aprameyo and de Vera-Piquero, Carlos},
     title = {Pullbacks of {Saito-Kurokawa} {Lifts} and a {Central} {Value} {Formula} for {Degree} 6 {\(L\)-Series}},
     journal = {Documenta mathematica},
     pages = {1935--2036},
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     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a16/}
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Pal, Aprameyo; de Vera-Piquero, Carlos. Pullbacks of Saito-Kurokawa Lifts and a Central Value Formula for Degree 6 \(L\)-Series. Documenta mathematica, Tome 24 (2019), pp. 1935-2036. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a16/