Report
A generalized PGL(2) Petersson/Bruggeman/Kuznetsov formula for analytic applications
| العنوان: | A generalized PGL(2) Petersson/Bruggeman/Kuznetsov formula for analytic applications |
|---|---|
| المؤلفون: | Hu, Yueke, Petrow, Ian, Young, Matthew P. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11F12, 11F30, 11F70, 11F72, 11F85 |
| الوصف: | We develop generalized Petersson/Bruggeman/Kuznetsov (PBK) formulas for specified local components at non-archimedean places. In fact, we introduce two hypotheses on non-archimedean test function pairs $f \leftrightarrow \pi(f)$, called geometric and spectral hypotheses, under which one obtains `nice' PBK formulas by the adelic relative trace function approach. Then, given a supercuspidal representation $\sigma$ of ${\rm PGL}_2(\mathbb{Q}_p)$, we study extensively the case that $\pi(f)$ is a projection onto the line of the newform if $\pi$ is isomorphc to $\sigma$ or its unramified quadratic twist, and $\pi(f) = 0$ otherwise. As a first application, we prove an optimal large sieve inequality for families of automorphic representations that arise in our framework. Comment: v2: Proof that p=2 principal series test function is a newform projector added, and a few very minor typos fixed |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2411.05672 |
| رقم الانضمام: | edsarx.2411.05672 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |