Related papers: Subconvexity for Symmetric Square L-functions off-…

Let $P$ be a prime and $k$ be an even integer. Let $f$ be a full level holomorphic cusp form of weight $k$ and $\rho$ be a primitive level $P$ holomorphic cusp form with arbitrary nebentypus and fixed weight $\kappa$. We prove a hybrid…

Let $F$ be a $G L(3)$ Hecke-Maass cusp form of prime level $P_1$ and let $f$ be a $G L(2)$ Hecke-Maass cuspform of prime level $P_2$. In this article, we will prove a subconvex bound for the $G L(3) \times G L(2)$ Rankin-Selberg…

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 $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or the Eisenstien series $E(z,1/2)$ and $\pi$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form with its Langlands parameter $\mu$ in generic position i.e. away from Weyl chamber walls and…

In this paper, we prove uniform bounds for $\rm GL (3)\times GL(2)$ $L$-functions in the $\rm GL(2)$ spectral aspect and the $t$ aspect by a delta method. More precisely, let $\phi$ be a Hecke--Maass cusp form for $\rm SL(3,\mathbb{Z})$ and…

Let $f$ be the Hecke eigenform for the modular group $SL_2(\mathbb{Z})$, and $L(s, \text{sym}^2 f)$ be the symmetric square $L$-function associated with $f$. For $\frac{1}{2}<\sigma<1$, define $m(\sigma)$ as the supremum of all numbers $m$…

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…

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 $f$ be a fixed self-contragradient Hecke-Maass form for $SL(3,\mathbb Z)$, and $u$ an even Hecke-Maass form for $SL(2,\mathbb Z)$ with Laplace eigenvalue $1/4+k^2$, $k>0$. A subconvexity bound $O\big(k^{4/3+\varepsilon}\big)$ in the…

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…

Let $f$ be a Maass cusp form for $\rm SL_2(\mathbb{Z})$ with Laplace eigenvalue $1/4+\mu_f^2$, $\mu_f>0$. Let $g$ be an arbitrary but fixed holomorphic or Maass cusp form for $\rm SL_2(\mathbb{Z})$. In this paper, we establish the following…

Let $q \in \mathbb{Z} [i]$ be prime and $\chi $ be the primitive quadratic Hecke character modulo $q$. Let $\pi$ be a self-dual Hecke automorphic cusp form for $\mathrm{SL}_3 (\mathbb{Z} [i] )$ and $f$ be a Hecke cusp form for $\Gamma_0 (q)…

We prove a sub-convex estimate for the sup-norm of $L^2$-normalized holomorphic modular forms of weight $k$ on the upper half plane, with respect to the unit group of a quaternion division algebra over $\mf Q$. More precisely we show that…

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass cusp form and $\chi$ be any non-trivial character $\bmod \, p$, where $p$ is prime. We show that the $L$-function associated…

Let $\pi$ be a Hecke-Maass cusp form for $\mathrm{SL(3, \mathbb{Z})}$ and $f$ be a holomorphic cusp form for $\mathrm{SL(2,\mathbb{Z})}$ of weight $k$ or a Hecke-Maass cusp form corresponding to the Laplacian eigenvalue $1/4+k^2$, $k\geq…

In this paper we obtain a sub-Weyl bound for $L(1/2+it,f)$ for $f$ a Hecke modular form.

Let $f$ and $g$ be holomorphic or Maass cusp forms for $\rm SL_2(\mathbb{Z})$ and let $\chi$ be a primitive Dirichlet character of prime power conductor $q=p^n$. For any given $\varepsilon>0$, we establish the following subconvexity bound…

Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime. In this note we revisit the subconvexity problem addressed in `The circle method and bounds…

Let $q$ be a large prime, and $\chi$ the quadratic character modulo $q$. Let $\phi$ be a self-dual Hecke--Maass cusp form for $SL(3,\mathbb{Z})$, and $u_j$ a Hecke--Maass cusp form for $\Gamma_0(q)\subseteq SL(2,\mathbb{Z})$ with spectral…

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…