Waldspurger formula over function fields

Chuang, Chih-Yun; Wei, Fu-Tsun

doi:10.1090/tran/7208

Waldspurger formula over function fields
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by Chih-Yun Chuang and Fu-Tsun Wei PDF

Trans. Amer. Math. Soc. 371 (2019), 173-198 Request permission

Abstract:

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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