Related papers: Bounds for $GL(3)\times GL(2)$ $L$-functions and G…

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 corresponding problem for $GL_{2}$ with ideas from…

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\otimes\chi)\ll_{f,q,\varepsilon}…

We give a sharp convexity estimate for L-functions which have a functional equation and an Euler product.

We employ a regularized relative trace formula to establish a second moment estimate for twisted $L$-functions across all aspects over a number field. Our results yield hybrid subconvex bounds for both Hecke $L$-functions and twisted…

For $L$-functions attached to automorphic representations of unitary groups $U_{n+1}\times U_n$, we establish a subconvex bound valid in certain horizontal aspects, where the set of ramified places is allowed to vary.

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $ \int_{\gamma}…

In this paper we study the subconvexity problem for the Rankin-Selberg L-function and triple product L-function, allowing joint ramifications and conductor dropping range. We first extend the method of Michel-Venkatesh to reduce the bounds…

We establish a subconvexity bound for a double Dirichlet series involving with the quadratic Hecke $L$-functions over the Gaussian field.

Let $M$ be a square-free integer and let $P$ be a prime not dividing $M$ such that $P \sim M^\eta$ with $0<\eta<2/21$. We prove subconvexity bounds for $L(\tfrac{1}{2}, f \otimes g)$ when $f$ and $g$ are two primitive holomorphic cusp forms…

We obtain a strong bound on the second moment of the $GL_3$ standard $L$-function on the critical line. The method builds on the recent work of Aggarwal, Leung, and Munshi which treated shorter intervals. We deduce some corollaries…

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…

Let $f$ and $g$ be two holomorphic or Hecke-Maass primitive cusp forms for $SL(2,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character of modulus $p$, an odd prime. A subconvex bound for the central values of the Rankin-Selberg…

Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $\chi$ be a primitive character of prime-power modulus $q = p^{\gamma}$. In this paper, we prove the following hybrid Weyl-type subconvexity bound…

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\GL_{1}$ and $\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present…

We establish sharp bounds for the second moment of symmetric-square $L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$, where the second moment is a sum over $t_j$ in a short interval. At the central point…

We give lower bounds of the conjectured order of magnitude for an orthogonal and a symplectic family of L-functions.

Let $M$ be a squarefree positive integer and $P$ a prime number coprime to $M$ such that $P\sim M^\eta$ with $0 < \eta < 2/5$. We simplify the proof of subconvexity bounds for $L(\frac{1}{2},f\otimes\chi)$ when $f$ is a primitive…

We develop an explicit Kuznetsov formula on GL(3) for congruence subgroups. Applications include a Lindelof on average type bound for the sixth moment of GL(3) L-functions in the level aspect, an automorphic large sieve inequality, density…

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid subconvex…

In this paper, we have proved Selberg's Central Limit Theorem for $GL(3)$ $L$-functions associated with the Hecke-Maass cusp form $f$. Moreover, we have proved the independence of the automorphic $L$-functions.