Bounds for twisted symmetric square $L$-functions - III

Abstract

Let $f$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell }$. Assume that $q$ is an odd prime. In this paper we prove the subconvex bound $$ L(\t1/2,\Sym f\otimesχ)\ll_{f,q,\varepsilon} q^{3\ell(1/4-1/36+\varepsilon)} $$ for any $\epsilon >0$. This can be compared with the recently established $t$-aspect subconvexity of the symmetric square $L$-functions.

arXiv comment12 pages. arXiv admin note: text overlap with arXiv:1203.0749

References in corpus (1)

• Bounds for twisted symmetric square $L$-functions

Cited by in corpus (6)

• Subconvexity for $GL(3)\times GL(2)$ twists (with an appendix by Will Sawin)
• Hybrid subconvexity bounds for twisted $L$-functions on $GL(3)$
• The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions
• Bounds for $G{L}_3$ $L$-functions in depth aspect
• The circle method and bounds for $L$-functions - III: $t$-aspect subconvexity for GL(3) $L$-functions
• Subconvexity for $GL(3)\times GL(2)$ $L$-functions in the depth aspect