相关论文: Weyl-type hybrid subconvexity bounds for twisted $…

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.

Let q be a prime and -D < -4 be an odd fundamental discriminant such that q splits in Q(\sqrt{-D}). For f a weight zero Hecke-Maass newform of level q and h the weight one theta series of level D corresponding to an ideal class group…

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…

We prove a Weyl-exponent subconvex bound for any Dirichlet $L$-function of cube-free conductor. We also show a bound of the same strength for certain $L$-functions of self-dual $\mathrm{GL}_2$ automorphic forms that arise as twists of forms…

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 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 $g$ 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 f be a Hecke-Maass or holomorphic primitive cusp form for $SL(2,\mathbb{Z})$ with Fourier coefficients $\lambda_{f}(n)$. Let $\chi$ be a primitive Dirichlet character of modulus p, where p is a prime number. In this article we prove the…

We describe a general method to obtain weak subconvexity bounds for many classes of $L$-functions. This has applications to a conjecture of Rudnick and Sarnak for the mass equidistribution of Hecke eigenforms (see arxiv.org:math/0809.1636).

We use a `trivial' delta method to prove the Weyl bound in $t$-aspect for the $\rm L$-function of a holomorphic or a Hecke-Maass cusp form of arbitrary level and nebentypus. In particular, this extends the results of Meurman and Jutila for…

In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic…

Let $f $ be a holomorphic Hecke eigenforms or a Hecke-Maass cusp form for the full modular group $ SL(2, \mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that \[ L…

Let $A$ be a central division algebra of prime degree $p$ over $\mathbb{Q}$. We obtain subconvex hybrid bounds, uniform in both the eigenvalue and the discriminant, for the sup-norm of Hecke-Maass forms on the compact quotients of…

We prove an upper bound for the twelfth moment of Hecke $L$-functions associated to holomorphic Hecke cusp forms of weight $k$ in a dyadic interval $T \leq k \leq 2T$ as $T$ tends to infinity. This bound recovers the Weyl-strength subconvex…

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

Let $f $ be a holomorphic Hecke eigenform or a Hecke-Maass cusp form for the full modular group $ SL(2, \mathbb{Z})$. In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$-functions. We shall prove that \[ L…

We establish a central limit theorem for the central values of Dirichlet $L$-functions with respect to a weighted measure on the set of primitive characters modulo $q$ as $q \rightarrow \infty$. Under the Generalized Riemann Hypothesis…

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 prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following {\em lower} bounds for its counting function. For $\la\ge \la_1$, one has N(\la) >…

We prove hybrid subconvexity bounds twisted L-functions $L(s,f\times \chi)$ at the central point using a fourth moment estimate, including a new instance of the Burgess subconvexity bound.