# A new subconvex bound for GL(3) L-functions in the t-aspect

@article{Aggarwal2019ANS, title={A new subconvex bound for GL(3) L-functions in the t-aspect}, author={Keshav Aggarwal}, journal={arXiv: Number Theory}, year={2019} }

We revisit Munshi's proof of the $t$-aspect subconvex bound for $\rm GL(3)$ $L$-functions, and we are able to remove the `conductor lowering' trick. This simplification along with a more careful stationary phase analysis allows us to improve Munshi's bound to, $$ L(1/2+it, \pi) \ll_{\pi, \epsilon} (1+|t|)^{3/4-3/40+\epsilon}. $$

## 14 Citations

Subconvexity for $GL_{3}(R)$ $L$-Functions via Integral Representations

- Mathematics
- 2020

We study the subconvexity problem for $GL_{3}(R)$ $L$-functions in the t-aspect using integral representations by combining techniques employed by Michel--Venkatesh in their study of the…

Strong subconvexity for self-dual $\mathrm{GL} (3)$ $L$-functions

- Mathematics
- 2021

In this paper, we prove strong subconvexity bounds for selfdual GL(3) L-functions in the t-aspect and for GL(3)×GL(2) L-functions in the GL(2)-spectral aspect. The bounds are strong in the sense that…

Uniform bounds for $\rm GL(3) \times GL(2)$ $L$-functions

- Mathematics
- 2021

Abstract. In this paper, we prove uniform bounds for GL(3) × GL(2) L-functions in the GL(2) spectral aspect and the t aspect by a delta method. More precisely, let φ be a Hecke–Maass cusp form for…

Hybrid subconvexity bounds for twists of $\rm GL (3)\times GL(2)$ $L$-functions

- Mathematics
- 2021

The subconvexity problem of automorphic L-functions on the critical line is one of the central problems in number theory. In general, let C denote the analytic conductor of the relevant L-function,…

Subconvexity for GL3(R) L-functions: The key identity via integral representations

- MathematicsJournal of Number Theory
- 2021

Abstract We study the subconvexity problem for GL 3 ( R ) L-functions in the t-aspect using integral representations by combining techniques employed by Michel–Venkatesh in their study of the…

UNIFORM SUBCONVEXITY BOUNDS FOR GL(3)×GL(2) L-FUNCTIONS

- 2021

The subconvexity problem of automorphic L-functions on the critical line is one of the central problems in number theory, which have very important applications to equidistribution problems. The…

hybrid subconvexity bounds for twists of $\rm GL(3)$ $L$-functions

- Mathematics
- 2021

Let π be a SL(3,Z) Hecke-Maass cusp form and χ a primitive Dirichlet character of prime power conductor q = p with p prime. In this paper we will prove the following subconvexity bound

Analytic Twists of GL3 × GL2 Automorphic Forms

- MathematicsInternational Mathematics Research Notices
- 2021

Let $\pi $ be a Hecke–Maass cusp form for $\textrm{SL}_3(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _{\pi }(n,r)$. Let $f$ be a holomorphic or Maass cusp form for…

Subconvexity for twisted GL(3) L-functions

- Mathematics
- 2021

Using the circle method, we obtain subconvex bounds for GL3 L-functions twisted by a character χ modulo a prime p, hybrid in the t and p-aspects.

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