Hybrid level aspect subconvexity for GL(2) × GL(1) Rankin-Selberg L-FunctionsArticle
Authors: Keshav Aggarwal 1,2; Yeongseong Jo 1,2; Kevin Nowland 1,2
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Keshav Aggarwal;Yeongseong Jo;Kevin Nowland
1 Mathematics Department, The Ohio State University
2 Department of Mathematics [Ohio State University]
Let M be a squarefree positive integer and P a prime number coprime to M such that P∼Mη with 0<η<2/5. We simplify the proof of subconvexity bounds for $L(\frac{1]{2}, f \otimes \chi)whenfisaprimitiveholomorphiccuspformoflevelPand\chiisaprimitiveDirichletcharactermoduloM$. 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.
Keywords: Special values of L-functions,Rankin-Selberg convolution,subconvexity,δ-method 2010 Mathematics Subject Classification 11F11,11F67,11L05,[MATH]Mathematics [math],[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]