相关论文: Hybrid bounds for ${\rm{GL}}(4)\times {\rm{GL}}(1)…

Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^k$ with $p$ prime. In this paper we will prove the following subconvexity bound $$…

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb{Z})$ and $\chi=\chi_1\chi_2$ a Dirichlet character with $\chi_i$ primitive modulo $M_i$. Suppose that $M_1$, $M_2$ are primes such that $\max\{(M|t|)^{1/3+2\delta/3},M^{2/5}|t|^{-9/20},…

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…

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 $\pi$ be a fixed Hecke--Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be a prime. Let $L(s,\pi\otimes \chi)$ be the $L$-function associated to $\pi\otimes…

In this paper, we solve the hybrid subconvexity problem for $\rm GL (3)\times GL (2)$ $L$-functions twisted by a primtive Dirichlet charater modulo $M$ (prime) in the $M$- and $t$-aspects. We also improve hybrid subconvexity bounds for…

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 $\pi$ be a $SL(3,\mathbb Z)$ automorphic form. Let $\chi=\chi_1\chi_2$ be a Dirichlet character with $\chi_i$ primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that $\sqrt{M_2}M^{4\delta}<M_1<M_2M^{-3\delta}$, where…

In this paper, we prove hybrid subconvexity bounds for $\rm GL_2\times \rm GL_2$ Rankin--Selberg $L$-functions twisted by a primitive Dirichlet character $\chi$ modulo a prime power, in the $t$ and depth aspects.

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 $g$ 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, $f$ 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…

For $f$ a primitive holomorphic cusp form of even weight $k \geq 4$, level $N$, and $\chi$ a Dirichlet character mod $Q$ with $(Q,N)=1$, we establish a new hybrid subconvexity bound for $L(1/2 + it, f_\chi)$, which improves upon all known…

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)…

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…

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 $\mathfrak{q}>2$ be a prime number, $\chi$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex…

Let $f$ be a Hecke-Maass cusp form for $SL_3(\mathbb{Z})$ and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa\geq 10$. We prove a subconvexity bound $$…

We prove strong hybrid subconvex bounds simultaneously in the $q$ and $t$ aspects for $L$-functions of selfdual $\mathrm{GL}_3$ cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds…

We give a Burgess-like subconvex bound for $L(s, \pi \otimes \chi)$ in terms of the analytical conductor of $\chi$, where $\pi$ is a $GL_2$ cuspidal representation and $\chi$ is a Hecke character.