eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2019-01-23
10.46298/hrj.2019.5112
5112
journal article
Hybrid level aspect subconvexity for GL(2) × GL(1) Rankin-Selberg L-Functions
Keshav Aggarwal
Yeongseong Jo
https://orcid.org/0000-0001-5546-8370
Kevin Nowland
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.
https://hrj.episciences.org/5112/pdf
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]