On central critical values of the degree four L -functions for GSp ( 4 ) : a simple trace formula

We establish a simple relative trace formula for GSp ( 4 ) and inner forms with respect to Bessel subgroups to obtain a certain Bessel identity. From such an identity, one can hope to prove a formula relating central values of degree four spinor L -functions to squares of Bessel periods as conjectured by Böcherer. Under some local assumptions, we obtain nonvanishing results, i.e., a global Gross–Prasad conjecture for ( SO ( 5 ), SO ( 2 )) .

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