Hybrid Level Aspect Subconvexity for $GL(2)\times GL(1)$ Rankin-Selberg $L$-Functions
- Resource Type
- Working Paper
- Authors
- Aggarwal, Keshav; Jo, Yeongseong; Nowland, Kevin
- Source
- Subject
- Mathematics - Number Theory
11F11 (Primary), 11F67, 11L05 (Secondary)
- Language
Let $M$ be a squarefree positive integer and $P$ a prime number coprime to $M$ such that $P\sim M^\eta$ with $0 < \eta < 2/5$. We simplify the proof of subconvexity bounds for $L(\frac{1}{2},f\otimes\chi)$ when $f$ is a primitive holomorphic cusp form of level $P$ and $\chi$ is a primitive Dirichlet character modulo $M$. These bounds are attained through an unamplified second moment method using a modified version of the delta method due to R. Munshi. The technique is similar to that used by Duke-Friedlander-Iwaniec save for the modification of the delta method.
Comment: Correct bounds for j-Bessel functions and add definition of Kloosterman sum associated to cups. Main result is not changed