相关论文: Hybrid Subconvexity Bound for $L\left(\frac{1}{2},…

\begin{abstract} In this article, we will get non-trivial estimates for the central values of degree six Rankin-Selberg $L$-functions $L(1/2+it, \pi \times f)$ associated with a ${GL(3)}$ form $\pi$ and a ${GL(2)} $ form $f$ using the delta…

Let $f$ be a newform of prime level $p$ with any central character $\chi\, (\bmod\, p)$, and let $g$ be a fixed cusp form or Eisenstein series for $\hbox{SL}_{2}(\mathbb{Z})$. We prove the subconvexity bound: for any $\varepsilon>0$,…

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…

We establish a Weyl-type subconvexity of $L(\tfrac{1}{2},f)$ for spherical Hilbert newforms $f$ with level ideal $\mathfrak{N}^2$, in which $\mathfrak{N}$ is required to be cube-free, and at any prime ideal $\mathfrak{p}$ with…

Let $f\in S_k(N,\psi)$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is a prime and $\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form $$…

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb Z)$ and $f$ be a holomorphic (or Maass) Hecke form for $SL(2,\mathbb{Z})$. In this paper we prove the following subconvex bound $$ L\left(\tfrac{1}{2}+it,\pi\times…

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)…

For a fixed cusp form $\pi$ on $\operatorname{GL}_3(\mathbb{Z})$ and a varying Dirichlet character $\chi$ of prime conductor $q$, we prove that the subconvex bound \[ L(\pi \otimes \chi, \tfrac{1}{2}) \ll q^{3/4 - \delta} \] holds for any…

Let $\Gamma$ be a cocompact, discrete, and irreducible subgroup of $\mathrm{PSL}_{2}(\mathbb{R})^{n}$. Let $\nu$ be a unitary character of $\Gamma$. For $k\in1\slash 2\,\mathbb{Z}$, let $\sknu$ denote the complex vector space of cusp forms…

Given a convex representation $\rho:\Gamma\to\textrm{PGL}(d,\mathbb{R})$ of a convex co-compact group $\Gamma$ of $\mathbb{H}^k$ we find upper bounds for the quantity $\alpha h_\rho,$ where $h_\rho$ is the entropy of $\rho$ and $\alpha$ is…

Let f be an $L^2$-normalized weight zero Hecke-Maass cusp form of square-free level N, character $\chi$ and Laplacian eigenvalue $\lambda\geq 1/4$. It is shown that $\| f \|_{\infty} \ll_{\lambda} N^{-1/37}$, from which the hybrid bound…

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 $\phi$ be a Hecke-Maass cusp form for $\mathrm{SL(3, \mathbb{Z})}$ with Langlands parameters $({\bf t}_{i})_{i=1}^{3}$ and $f$ be a holomorphic or Hecke-Maass cusp form for $\mathrm{SL(2,\mathbb{Z})}$. In this article, we prove the…

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…

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on $ {\mathbb H}^{n+1}$: in strips parallel to the imaginary axis the zeta function is bounded by $ \exp (C |s|^\delta) $ where $ \delta $…

The classical result of Patterson and Sullivan says that for a non-elementary convex cocompact subgroup $\Gamma<\text{SO}^\circ (n,1)$, $n\ge 2$, the Hausdorff dimension of the limit set of $\Gamma$ is equal to the critical exponent of…

We prove hybrid subconvexity bounds for a wide class of twisted L-functions $L(s,f\times \chi)$ at the central point, including a new instance of the Weyl subconvexity bound.

We give an upper bound for the error term in the Hardy-Ramanujan-Rademacher formula for the partition function. The main input is a new hybrid subconvexity bound for the central value $L(\tfrac 12,f\times (\tfrac{q}{\cdot}))$ in the $q$ and…

Modifying a method of Jutila, we prove a t aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus…

Let $F$ be a number field with adele ring $\mathbb{A}_F$, $\pi_1, \pi_2$ be two unitary cuspidal automorphic representations of $\mathrm{PGL}_2(\mathbb{A}_F)$ with finite analytic conductor. We study the twisted first moment of the triple…