English

Subconvexity for Symmetric Square L-functions off-centre

Number Theory 2023-02-15 v1

Abstract

Let pp be a prime. Let ff be a holomorphic modular form of level pp with trivial nebentypus. We prove the bound L(sym2f,12+it)f,ϵp1/2+ϵt3/41/12+ϵL\left(\text{sym}^2f, \frac{1}{2} + it\right) \ll_{f,\epsilon} p^{1/2+\epsilon}t^{3/4-1/12 + \epsilon}. This bound is subconvex in the tt-aspect and almost convex in the level aspect simultaneously.

Keywords

Cite

@article{arxiv.2302.07236,
  title  = {Subconvexity for Symmetric Square L-functions off-centre},
  author = {Mayukh Dasaratharaman and Ritabrata Munshi},
  journal= {arXiv preprint arXiv:2302.07236},
  year   = {2023}
}

Comments

First Draft. Comments welcome

R2 v1 2026-06-28T08:40:07.056Z