通过布鲁哈特分解的 $(text{GL}_2, \text{GL}_2)$θ 升维的明确公式

arXiv - MATH - Number Theory Pub Date : 2024-09-11 DOI:arxiv-2409.06940

Peter Xu

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引用次数: 0

摘要

利用克罗内克-爱森斯坦数列的权重-1 和权重-2 组合来构造平方椭圆曲线的分布德拉姆复数中的电流，我们找到了无需平滑的第二类$(\text{GL}_2,\text{GL}_2)$ θ提升的简单明确公式，类似于西格尔关于爱森斯坦数列周期的经典公式。对于 $K$ 一个 CM 场，同样的技术无需改变即可得到类似的 $(\text{GL}_2(K),K^\times)$ theta 对应关系式。

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Explicit formula for the $(\text{GL}_2, \text{GL}_2)$ theta lift via Bruhat decomposition

Using combinations of weight-1 and weight-2 of Kronecker-Eisenstein series to construct currents in the distributional de Rham complex of a squared elliptic curve, we find a simple explicit formula for the type II $(\text{GL}_2, \text{GL}_2)$ theta lift without smoothing, analogous to the classical formula of Siegel for periods of Eisenstein series. For $K$ a CM field, the same technique applies without change to obtain an analogous formula for the $(\text{GL}_2(K),K^\times)$ theta correspondence.

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arXiv - MATH - Number Theory

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