Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01986708v1

Published on: January 23, 2019

Submitted on: January 23, 2019

Keywords: Special values of L-functions,Rankin-Selberg convolution,subconvexity,δ-method 2010 Mathematics Subject Classification 11F11,11F67,11L05,
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MATH
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Mathematics [math],
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MATH.MATH-NT
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Mathematics [math]/Number Theory [math.NT]