Refined global Gan-Gross-Prasad conjecture for Bessel periods. (English) Zbl 1404.11065
Summary: We formulate a refined version of the global Gan-Gross-Prasad conjecture for general Bessel models, extending the work of A. Ichino and T. Ikeda [Geom. Funct. Anal. 19, No. 5, 1378–1425 (2010; Zbl 1216.11057)] and R. N. Harris [Int. Math. Res. Not. 2014, No. 2, 303–389 (2014; Zbl 1322.11047)] in the co-rank 1 case. It is an explicit formula relating the automorphic period of Bessel type and the central value of certain \(L\)-function. To support such conjecture, we provide two examples for pairs \(\mathrm{SO}_{5}\times\mathrm{SO}_{2}\) and \(\mathrm{SO}_{6}\times\mathrm{SO}_{3}\) (both co-rank 3) in the endoscopic case via theta lifting.
MSC:
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11F55 | Other groups and their modular and automorphic forms (several variables) |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
Keywords:
Bessel periods; Gan-Gross-Prasad conjecture; automorphic periods; central values; \(L\)-functionsReferences:
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