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arXiv · 1611.02601

Waldspurger formula over function fields

Chih-Yun Chuang·Fu-Tsun Wei
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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 $SO(3)$ over function fields.

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Chih-Yun Chuang, Fu-Tsun Wei. 2016-11-08. Waldspurger formula over function fields. https://arxiv.org/abs/1611.02601

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