**Title**: Bounds for twists of $\rm GL(3)$ $L$-functions

**Speaker**: Yongxiao Lin (Ohio State University)

**Abstract**: In this talk, we will discuss nontrivial estimates for certain degree 3 $L$-functions on the critical line. The $L$-functions we are particularly interested in are $L(s,\pi)$ and $L(s,\pi\otimes \chi)$, where $\pi$ is a fixed Hecke-Maass cusp form for $\rm{SL}(3,\mathbb{Z})$ and $\chi$ is a primitive Dirichlet character of conductor $q$ (which we assume to be a prime). We will describe our work in estasblishing $t$-aspect subconvex bound for $L\left(1/2+it,\pi \right)$, and the conductor and $t$ aspects subconvex bound for $L(1/2+it, \pi\otimes \chi)$, under the assumption $q^{\varepsilon} < |t| < q^{34/21}$. Time permitting, we shall give a sketch of the proof for a subconvex bound $L\left(1/2+it,\pi \right)\ll (|t|+2)^{3/4-\delta}$, where $\delta=1/60-\varepsilon$.

**Seminar URL**: https://research.math.osu.edu/numbertheory/number.php