The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B

Ritabrata Munshi

The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B

Number Theory 2014-02-18 v2

Authors: Ritabrata Munshi

Abstract

Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\chi$ be a primitive Dirichlet character modulo $M$ , which we assume to be prime for simplicity. We will prove the following subconvex bound $L\left(\tfrac{1}{2},\pi\otimes\chi\right)\ll_{\pi,\varepsilon} M^{\frac{3}{4}-\frac{1}{1612}+\varepsilon}.$

Keywords

circle method subconvexity gl(3) l-functions twists hecke-maass cusp forms dirichlet character ramanujan conjecture

Cite

@article{arxiv.1311.6120,
  title  = {The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B},
  author = {Ritabrata Munshi},
  journal= {arXiv preprint arXiv:1311.6120},
  year   = {2014}
}

Comments

Second draft: 36 pages, several minor errors corrected

The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B

Abstract

Keywords

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