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TheStudent
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Bound for orbital integrals

Let $F$ be a number field, and $G$ be the group of units of a quaternion algebra $D$ over $F$. At a certain ramified place $v$, for $\gamma_v \in G(F_v)$, could we bound the orbital integral $$\mathcal{O}_{\gamma_v}(MC(\pi_v))$$

where $MC(\pi_v)$ is the matrix coefficient attached to $\pi_v$? I am seeking for a bound in terms of the Plancherel measure of $\pi_v$.

TheStudent
  • 937
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  • 8