Waldspurger formula over function fields Article Swipe
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Chih-Yun Chuang
,
Fu‐Tsun Wei
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1090/tran/7208
· OA: W2556448246
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1090/tran/7208
· OA: W2556448246
In this paper, we derive a function field version of the Waldspurger formula for the central critical values of the Rankin-Selberg $L$-functions. This formula states that the central critical $L$-values in question can be expressed as the "ratio" of the global toric period integral to the product of the local toric period integrals. Consequently, this result provides a necessary and sufficient criterion for the non-vanishing of these central critical $L$-values, and supports the Gross-Prasad conjecture for $\mathrm {SO}(3)$ over function fields.
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