Hybrid level aspect subconvexity for GL(2) × GL(1) Rankin-Selberg L-Functions

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 primiti...

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Bibliographic Details
Published inHardy-Ramanujan Journal Vol. Atelier Digit_Hum; pp. 104 - 117
Main Authors Aggarwal, Keshav, Jo, Yeongseong, Nowland, Kevin
Format Journal Article
LanguageEnglish
Published Hardy-Ramanujan Society 23.01.2019
Subjects
Mathematics
Number Theory
11L05
Rankin-Selberg convolution
Special values of L-functions
subconvexity
δ-method 2010 Mathematics Subject Classification 11F11
11F67
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Summary: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.
ISSN:2804-7370
2804-7370
DOI:10.46298/hrj.2019.5112