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arXiv · 1605.05625

Hybrid Level Aspect Subconvexity for $GL(2)\times GL(1)$ Rankin-Selberg $L$-Functions

Keshav Aggarwal·Yeongseong Jo·Kevin Nowland
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Abstract

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.

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Keshav Aggarwal, Yeongseong Jo, Kevin Nowland. 2016-05-18. Hybrid Level Aspect Subconvexity for $GL(2)\times GL(1)$ Rankin-Selberg $L$-Functions. https://arxiv.org/abs/1605.05625

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