论文标题
Prasad的拆分案例 - takloo-bighash猜想，用于零等级表示
The split case of the Prasad--Takloo-Bighash conjecture for cuspidal representations of level zero
论文作者
论文摘要
令$ e/f $为非阿基米德人本地田地的二次扩展，具有奇数残留特征。对于$ \ mathrm {gl}（2m，f）$的cuspidal表示，我们证明了Prasad和Takloo-Bighash的猜想。该猜想的特征是对$ $（\ mathrm {gl}（2m，f），\ mathrm {gl}（m，e））$的区别，相对于字符$ \ circ \ circ \ circ \ circ \ circ \ mathrm {det} $ of $ \ \ \ \ \ m m mathrm {gl}（m，e）$，在某些条件上，在某些条件上，尤其是在某些条件上。当$ e/f $不受影响时，当$ e/f $ tame tame时，我们还计算所涉及的eprivariant线性形式的多样性。在这两种情况下，这种多重性最多都是一种。
Let $E/F$ be a quadratic extension of non archimedean local fields of odd residual characteristic. We prove a conjecture of Prasad and Takloo-Bighash, in the case of cuspidal representations of depth zero of $\mathrm{GL}(2m,F)$. This conjecture characterizes distinction for the pair $(\mathrm{GL}(2m,F),\mathrm{GL}(m,E))$ with respect to a character $μ\circ \mathrm{det}$ of $\mathrm{GL}(m,E)$, in terms of certain conditions on Langlands paremeters, including an epsilon value. We also compute the multiplicity of the involved equivariant linear forms when $E/F$ is unramified, and also when $μ$ is tame. In both cases this multiplicity is at most one.
